Problems on Time and Work

Problems on Time  and Work

Q. 1. A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be

(a) 8    (b) 6    (c) 7    (d) 5    (e) None of these

Ans: (a) 8

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Therefore, here, the required number of days = 12 × 24/ 36 = 8 days. Ans.

Q. 2. If  4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in

(a)  1 day   (b) 1 ½ days  (c) ¾ day      (d) ½ day     (e) None of these

Ans: (a) 1 day

Explanation:

The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m

No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. Ans.

Q. 3. If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in

(a) 7 days    (b) 6 days   (c) 4 days     (d) 3 days    (e) None of these

Ans:  (d) 3 days.

Explanation:

That is, 1 person can do one time of the work in 3 days.

Therefore, 7 persons can do 7 times work in the same 3 days itself. Ans.

Q. 4. Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is

(a) 15    (b) 10    (c) 9     (d) 8     (e) None of these

Ans: ( d) 8

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

That is, the required No. of days = 10 × 40/50 = 8 days. Ans.

Q. 5. 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required

(a) 4   (b) 5   (c) 6    (d) 8   (e) None of these

Ans: (d) 8

Explanation:

That is, 1 work done  = 12 × 8 × 10

Then, 12  8 × 10 = ? × 15 × 8

? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days. Ans.

Q. 6. If  5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in

(a) 25 days   (b) 20 days    (c) 15 days   (d) 10 days   (e) None of these

Ans:  (a) 25 days

Explanation:

That is, half the work done = 5 × 15 × ½

Then, 5 × 15 × ½  = 3 × ? ×1/2

i.e. 5  × 15 = 3 × ?

therefore, ? (No. days required) = 5 × 15/3 = 25 days. Ans.

Q. 7. 30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be

(a) 15    (b) 21    (c) 25    (d) 22    (e) None of these

Ans:  (b) 21

Explanation:

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30

? (No. of labourers) = 30 × 7 × 18/6 × 30

                                = 21. Ans.

Q. 8. If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be

(a) 20 days    (b) 10 days     (c) 14 days    (d) 15 days    (e) None of days

Ans: (d) 15 days

Explanation:

That is,  5 × 9 = 3 × ?

? = 5 × 9/3 = 15 days. Ans.

Q. 9. A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?

(a) 10 hours    (b) 20 hours    (c) 30 hours    (d) 40 hours   (e) None of these

Ans: (c) 30 hours

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore, the No. of hours required by B  = 10 × 15/ 15 – 10 = 150/5 = 30 hours. Ans.

Q. 10. 16 men or 20 women can finish a work in 25 days. How many days 28 men and 15 women will take to finish this job?

(a) 19  13/43 days      (b) 11 27/43 days     (c) 8 days   (d) 10 days    (e) None of these

Ans: (d) 10 days

Explanation:

16 men = 20 women

Therefore, 1 women = 16/20 men = 4/5 men

15 women = 4/5 × 15 men = 12 men

i.e. 28 men + 15 women = 28 men + 12 men = 40men

1 work done by men = 16 × 25

16 × 25 = 40 × ?

 ? (  no. of days) = 16 × 25/40 = 10 days. Ans.

Q. 11. A can do a piece of work in 5 days and B can do the same work in 10 days. How many days will both take to complete the work?

(a) 5 days    (b) 3 1/3 days     (c) 3 days     (d) 6 days    (e) None of these

Ans: (b) 3 1/3 days

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

That is, the required No. of days = 5 × 10/15 = 3 1/3 days. Ans.

Q. 12. If 12 men can do a piece of work in 24 days, then in how many days can 18 men do the same work?

(a) 36     (b) 20     (c) 18     (d) 16    (e) None of these

Ans: (d) 16

Explanation:

1 work done = 12 × 24

Then, 12 × 24 = 18 × ? days

? days = 12 × 24/18 = 16. Ans.

Q. 13. A group of workers accepted to do a piece of work in 25 days. If 6 of them did not turn for the work and the remaining workers did the work in 40 days, then the original number of workers was

(a) 22    (b) 20     (c) 18      (d) 16     (e) None of these

Ans:  (d) 16

Explanation:

Let the original number of workers be ‘x’

Then,  x × 25 = (x – 6) × 40

          25x = 40x -240

240 = 40x -25x = 15x

x = 240/15 = 16. Ans.

Q. 14. If 8 men or 12 women can do a piece of work in 10 days, then the number of days required by 4 men and 4 women to finish the work is

(a) 8    (b) 10     (c) 12     (d) 4     (e) None of these

Ans:  (c) 12

Explanation:

8 men = 12 women

1 woman = 8/12 men = 2/3 men

4 women = 2/3 × 4 men = 8/3 men

4 men + 4 women = 4 + 8/3 men = 20/3 men

1 work done = 8 × 10

8 × 10 = 20/3 × ?days

?days = 8 × 10 × 3/20 = 12 days. Ans.

Q. 15. If 8 men can dig a well in 18 days, then the number of days, 12 men will take to dig the same well will be

(a) 12 days   (b) 10 days    (c) 8 days    (d) 16 days    (e) None of these

Ans: (a) 12 days

Explanation:

Work done = 8 × 18

Then, 8 × 18 = 12 × ? days

? days = 8 × 18/12 = 12 days. Ans.

Q. 16. 39 men can repair a road in 12 days working 5 hours a day. In how many days will 30 men working 6 hours peer day complete the work?

(a) 10    (b) 13   (c) 14     (d) 15      (e) None of these

Ans: (b) 13

Explanation:

1 work done = 39 × 12 × 5

39 × 12 × 5 = 30 × 6 × ?days

? days = 39 × 12 × 5/ 30 × 6 = 13 days. Ans.

Q. 17. A certain number of men can do a work in 40days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially?

(a) 30   (b) 24    (c) 16    (d) 20    (e) None of these

Ans: (b) 24

Explanation:

Let ‘x’ be the initial number of men

Then, 1 work done = x × 40

Then, x × 40 = (x + 8 ) (40 – 10)

         40x = 30x + 240

10x = 240

Therefore, x = 240/10 = 24 men. Ans.

Q. 18. If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work?

(a) 10 days    (b) 6 days    (c) 4 days    (d) 3 days    (e) None of these

Ans:  (b) 6 days

Explanation:

4 men = 6 boys

Then,  1 boy = 4/6 men = 2/3 men

11 boys = 2/3 × 11 men = 22/3 men

Then, 6 men + 11 boys = 6 + 22/3 men = 40/3 men

1 work done = 4 men × 20days

That is, 4 × 20 = 40/3 × ? days

? days = 4 × 20 × 3/40 = 6 days. Ans.

Q. 19. A works twice as fast as B. if B can complete a work in 12 days independently. The number of days in which A and B can together finish the work?

(a) 18 days    (b) 8 days    (c) 6 days     (d) 4 days    (e) None of these

Ans: (d) 4 days

Explanation:

If B takes 12 days to finish the work, then A takes 6 days to finish the same work.

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Therefore, the Number of days taken by A and B together to finish the same work = 6 × 12/18

                                                                                                                  = 4 days. Ans.

Q. 20. A and B can do a piece of work in 4 days. If A can do it alone in 12 days, B will finish the work in

(a) 4 days   (b) 6 days    (c) 8 days   (d) 10 days   (e) None of these

Ans:  (b) 6 days

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore, the number of days B will take to finish the work = 4 × 12/ 12 – 4

                                                                                                 = 48/8 = 6 days. Ans.

Q. 21. 5 men can do  a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it?

 (a) 4    (b) 5     (c)  6    (d) 8   (e) None of these

Ans:  (b) 5

Explanation:

5men × 6 = 10 women × 5

30 men   = 50 women

1 woman = 30/50 men = 3/5 men

5 women = 3/5 × 5 men = 3 men

5 women + 3 men = 3 + 3 = 6 men

That is, 1 work done = 5 × 6

5 × 6 = 6 × ?days

? days = 5 × 6/6  = 5 days. Ans.

Q. 22. A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days then, the original number of workers was

(a) 100   (b) 110   (c) 55     (d) 50    (e) None of these

Ans: (b) 110

Explanation:

Let ‘x’ be the original number of workers

Then, x × 100 = ( x – 10) 110

100 x = 110x – 1100

1100 = 10 x

 x = 110. Ans.

Q. 23. A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10  women in 6 days. How many days are needed to completed the job if the two teams work together?

(a) 4    (b) 6     (c) 9   (d) 18   (e) None of these

Ans: (a) 4

Explanation:

Consider men’s work days as one group and women’s working days as other group

Then, the required No. of days = 12 × 6/18 = 4 days. Ans.

Q. 24. A can do a piece of work in 12 days, while B can do it in 8 days with the help of C, they finish the work in 4 days. Then C alone can do the work in

(a) 24 days   (b) 20 days    (c) 16 days    (d) 4 days    (e) None of these

Ans: (a) 24 days

Explanation:

A and B together can do the work in  12 × 8/20 = 96/20 days

  A +B and C together do the work in 4 days.

Then C alone can do the work in  96/20 × 4/96/20 – 4 days

                                   = 96/5/16/20 = 96/5 × 20/16 = 24 days. Ans.

Q. 25. A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the job if 6 men leave after working for 6 days?

(a) 3    (b) 12   (c) 6     (d) 24      (e) None of these

Ans:  (c) 6

Explanation:

Half the work is done by 12 men in 6 days.

Remaining half should be done by 6 men in ? days

Then,  12 × 6 × ½ = 6 × ?days × ½

          36 = 3 × ?days

? days = 36/3 =12 days

Extra days required = 12 -6 = 6 days. Ans.

Q. 26. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take, worker A and worker B, working together but independently, do the same job?

(a) 4 1/9 hours   (b) 4 2/9 hours   (c) 4 4/9 hours     (d) 4 5/9 hours    (e) None of these

Ans: (c) 4 4/9 hours

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Then 8 × 10/18 = 4 4/9 hours. Ans.

Q. 27. Three workers working all days can do a work in 10 days. But one of them having other employment can work only half time. In how many days the work can be finished?

(a) 15  days    (b) 16 days    (c) 12 days      (d) 12.5 days       (e) None of these

Ans: (c) 12 days.

Explanation:

Sum of each persons’ one day’s work = 1/3 ×10 + 1/3 ×10 + 1/3× 20 = 1/30 + 1/30 + 1/60

                                                                    = 5/60 = 1/12

Therefore, the work can be finished in 12 days. Ans.

Q. 28. Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed?

(a) 9 days    (b) 8 1/3 days     (c) 8 days    (d) 6 1/3 days    (e) None of these

Ans: (a) 9 days

Explanation:

The work done by the three persons in 3 days ( because Sam works only on every third day)

                                                                           =  3/15 + 1/10 + 1/30 = 6 + 3 + 1/30 = 10/30

                                                                           = 1/3 of the work

Therefore, the job will be completed in 3 × 3 = 9 days. Ans.

Q. 29. Prakash alone can complete a job in 12 hours, Jayant alone can complete the same job in 6 hours. How many hours will they take together to complete the job?

(a) 4    (b) 6    (c) 2     (d) 8     (e) None of these

Ans:  (a) 4

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Here, the No. of hours required to complete the work , working together = 12 × 6/18

                                                                                                                    = 4 hours. Ans.

Q. 30. 56 men completes a work in 12 days. How many men will be required to complete the work in 16 days?

(a) 38     (b) 24    (c) 42     (d) 48    (e) None of these

Ans:  (c) 42

Explanation:

1 work done = 56 men × 12 days

Then, 56 ×12 = ? men × 16

? men = 56 × 12/16 = 42 men. Ans.

Q. 31. Six men or tern boys can do a piece of work in fifteen days. How long would it take for 12 men and 5 boys to do the same piece of work?

(a) 6 days     (b) 28 days      (c) 25 days    (d) 7 days     (e) None of these

Ans: (a) 6 days

Explanation:

6 men = 10 boys

Then, 1 boy = 6/10 men =  3/5 men

Then, 5 boys = 3/5 × 5 = 3 men

12 men + 5 boys = 15 men

1 work done = 6 men × 15 days

Therefore,  6 × 15 = 15 × ? days

? days = 6 × 15/15 = 6 days. Ans.

Q. 32. If  4 workers can make 42 toys in 6 days, how many toys can 12 workers make in 3 days?

(a) 63    (b) 28    (c) 252   (d) 7    (e) None of these

Ans: (a) 63

Explanation:

4 workers in 3 days make 21 toys,

Then, 1 worker can make 21/4 toys in 3 days

Therefore, No. of toys made by 12 workers in 3 days = 21/4 × 12 = 63 toys. Ans.

Q. 33. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will work get completed?

(a) 6    (b) 7 2/3     (c) 6 2/3     (d) 6 1/3    (e) None of these

Ans: (c) 6  2/3

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Here, men’s working days can be taken as A  and that of women as B

Then, 15 × 12/27 = 6 2/3 days.Ans.

Q. 34.  Three men, four women and six children can complete a work in 7 days . A woman does double the work a man does and a child does half the work a man does. How many women can complete this work in  7 days?

(a) 8    (b) 7    (c) 12    (d) 10    (e) None of these

Ans: ( b)  7

Explanation:

3 men = 3/2 women

1 child = 1/2/2 = ¼ woman

Then, 6 children = ¼ × 6 = 6/4 = 3/2 women

Then, 3/2 women + 4 women + 3/2 women = 7 women

7 women does the work in 7 days.

Therefore, the No. of women required to finish the work in  7days = 7. Ans

Q. 35.  A sum of money is sufficient to pay P’s wages for 25 days or Q’s wages for 30 days. The money is sufficient to pay the wages of both for

(a) 13 5/11 days    (b) 13 days   (c) 13 6/11 days   (d) 13  7/11 days   (e) None of these

Ans: (d) 13 7/11

Explanation:

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Here, wages can be taken as days,

Then, 25 ×30/ 55 = 13 7/11 days. Ans.

Q. 36. A certain number of men complete a piece of work in 50 days. If there were 8 men more the work could be finished in 10 days less. How many men were originally there?

(a) 40    (b) 50    (c) 32    (d) 25    (e) None of these

Ans: (c) 32

Explanation:

Let the original No. of men = x

 Then, I work done = 50x

Then, 50x = (x + 8) 40

50x = 40x + 320

10 x = 320

x = 320/10 = 32 men. Ans.

Q. 37. A and B together finish a work in 30 days they worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. B alone can finish the work in

(a) 48 days   (b) 50 days  (c) 54 days (d) 60 days   (e) none of these

Ans: ( d) 60 days

Explanation:

(A + B)’s 1 days work = 1/30

A+B ‘s 20 days work = 1/30 × 20 = 2/3

Remaining work = 1 -2/3 = 1/3

1/3 of the work is done by A in 20 days

Therefore, A can complete the full work in 3 × 20 = 60 days

So, A’s 1 day’s work = 1/60

Then, B’s 1 day work = 1/30 – 1/60 = 1/60

Therefore, B can complete the work in 60 days. Ans.

Q. 38. A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work together and are forced to leave after 2 days. The time  taken to complete the remaining work is

(a) 13 days   (b) 10 days   (c) 9 days    (d) 6 days    (e) None of these

Ans: (d) 6 days

Explanation:

A’s 1 day work = 1/9

B’s 1 day work = 1/10

C’s 1 day work = 1/15

B + C ‘ s 1 day work = 1/10 + 1/15 = 1/6

B + C’s 2 day’s work = 1/6 × 2 = 1/3

The work remaining = 1 – 1/3 = 2/3

A can do the full work in 9 days.

So, the remaining 2/3 of the work is done by A in 2/3 × 9 days = 6 days. Ans.

Q. 39. If 40 men working 9 hours a day can finish a work in 21 days, in how many days will 27 men working 10 hours a day do the same work?

(a) 20 days   (b) 28 days   (c) 29 days    (d) 25 days   (e) None of these

Ans:  (b) 28 days

Explanation:

That is, 1 work done = 40 × 9 × 21

Then, 40 × 9 × 21 = 27 × 10 × ? days

Therefore, ? days = 40× 9 × 21 /27 × 10 = 28 days. Ans.

Q. 40. 8 children and 12 men complete a certain piece of work in 9 days. Each child takes twice the time taken by a man to finish the work. In how many days will 12 men finish the same work?

(a) 8   (b) 15    (c) 9    (d) 12   (e) None o f these

Ans: (d) 12

Explanation:

8 children = 4men

Then, 4 + 12 = 16 men completes the job in 9 days

Then, 16 × 9 = 12 × ? days

? days = 16 × 9/12 = 12 days. Ans.

Q. 41. Rajesh and Ajay can complete a job in 16 days. Rajesh alone can do it in 24 days. How long will Ajay alone take to finish the whole work?

(a) 20 days   (b) 48 days  (c) 30 days   (d) 36 days    (e) 28 days

Ans: (b) 48 days

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Then, Ajay alone can finish the whole work in, 16 × 24/24 – 16 = 16 × 24/8 = 48 days.Ans.

Q. 42. Ram, Shyam and Mohan can do a piece of work in 12, 15 and 20 days respectively. How long will they take to finish it together?

(a) 10 days   (b) 12 days    (c) 14 days   (d) 8 days    (e) 5 days

Ans: (e) 5 days

Explanation:

When A, B and C can do a work in x, y and z days respectively. Then, the three of them together can finish the work in  xyz/ x y + y z + x z  days

Therefore, the No. of days taken by them together  to finish the whole work

                   = 12 × 15 × 20/12 × 15 + 15 × 20 + 12 × 20

                  = 12 × 15 × 20/720 = 5 days. Ans.

Q. 43. Tapas works twice as much as Mihir. If both of them finish the work in 12 days, Tapas alone can do it in:

(a) 20 days   (b) 24 days     (c) 18 days    (d) 20 days   (e) None of these

Ans: (c)18 days

Explanation:

Mihir = 2 Tapas   (Consider, Tapas as ‘T’  and Mihir as “M”)

So, T ×2 T/ T + 2T = 12

2 T × T/3 T = 12

2 T = 3 × 12 = 36

T = 36/2 = 18 days i.e. No. of days taken by Tapas alone = 18 days. Ans.

Q. 44. Xavier can do a job in 40 days. He worked on it for 5 days and then Paes finished it in 21 days. In how many days Xavier and Paes can finish the work?

(a) 10   (b) 15   (c) 20   (d) 840/61     (e) 12

Ans: (b) 15

Explanation:

Xavier’s one day’s work = 1/40

His 5 days work = 1/40 × 5 = 1/8

The work remaining = 1 – 1/8 = 7/8

7/8 of the work is done by Paes in 21 days

Then, his 1 day’s work = 7/8/21 = 7/21 × 8 = 1/24

Therefore, the time taken by Paes to finish the whole work = 24 days.

Then. The No. of days two of them together take to finish the work =  40 × 24/40 + 24

                                                                            = 40 × 24/64 = 15 days. Ans.

Q. 45. A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?

(a) 1/6    (b) 1/9    (c) 2/5      (d) 2/7   (e) None of these

Ans: (a) 1/6

Explanation:

B alone can do the same work in 9 days

So, the No. of days both of them together take to do the work = 18 × 9/ 18 + 9

                                     =18 × 9/27 =   6 days.

The part of the work, they together finish in one day = 1/6. Ans.

Q. 46. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

(a) 1/24 day   (b) 7/24 day    (c) 3 3/7 days    (d) 4 days   (e) None of these

Ans:  (c) 3 3/7 days

Explanation:

When A, B and C can do a work in x, y and z days respectively. Then, the three of them together can finish the work in  xyz/ x y + y z + x z  days

Therefore, the No. of days taken by them together = 24 × 6 × 12/24 × 6 + 6 × 12 + 24 × 12

                                    = 24 × 6 × 12/ 504 = 3 3/7 days. Ans.

Q. 47. A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?

(a) 6 ½ days   (b) 7 days   (c) 7 ½ days    (d) 8 days   (e) None of these

Ans:  (c) 7 ½ days

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore, his son alone can do the work in 3 × 5/ 5 – 3 = 15/2 = 7 ½ days. Ans.

Q. 48. A works twice as fast as B. if B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is:

(a) 4 days    (b) 6 days    (c) 8 days    (d) 18 days     (e) None of  these

Ans: (a) 4 days

Explanation:

That is, if b alone can finish the work in 12 days,

A alone can finish the work in 6 days.

If  A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.

Therefore,

A and B can together finish the work in  6 × 12/18 days = 4 days. Ans.

Q. 49. A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is:

(a) 11   (b) 21    (c) 28     (d) 42     (e) None of these

Ans: (b) 21

Explanation:

A’s work is twice as B’s work

So, we can consider 2A = B

Then, A × 2A/ A+ 2A = 14

2A × A/ 3A = 14

2 A = 14  × 3

A = 21 days. i.e. A alone can finish the work in 21 days. Ans.

Q. 50. A is thrice as good a  workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

(a) 20 days    (b) 22 ½ days    (c) 25 days    (d) 30 days    (e) None of these

Ans: (b) 22 ½ days

Explanation:

That is, 3A = B, replacing 3 A in place of B, we get

3A – A = 60 days

A = 30 days, i.e. A alone can finish the work in 30 days

Then, B alone can finish the work in 3 ×30 = 90 days

Therefore, working together they can finish it in 30 × 90/ 120 days. = 22 ½ days. Ans.

Q. 51. A and B can do a job together in 7 days. A is 1 ¾ times as efficient as B. the same job can be done by A alone in:

(a) 9  1/3 days    (b) 11 days   (c) 12 ¼ days     (d) 16 1/3 days    (e) None  of these

Ans: (b) 11 days

Explanation:

 1 ¾ = 7/4

7/4 A = B, replacing B by 7/4 A, we get

A × 7/4 A/ A + 7/4 A = 7days

7 A × A/4 / 11A/4 = 7 A × A/ 11 A = 7A /11 = 7

A = 77/7 = 11,  So, A alone can finish the work in 11 days. Ans.

Q. 52. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

(a) 15    (b) 16    (c) 18    (d) 25    (e) None of these

Ans: (b) 16

Explanation:

The ratio of their efficiency, i.e. Sakshi : Tannya = 100 : 125 = 4 : 5

Therefore, ratio of time taken by them = 5 : 4

That is, No. of days taken by Sakshi is 5 units of ratio = 20 days

So, 1 unit of ratio = 20/5 = 4 days

Therefore, No. of days taken by Tannya = 4 × 4  = 16 days. Ans.

Q. 53. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

(a) 11 days   (b) 13 days    (c) 20 3/17 days    (d) 14 days  (e) None of these

Ans: (b) 13 days

Explanation:

The ratio of their efficiency =  A : B = 130 : 100 = 13 : 10

Therefore, the ratio of the time taken by them = 10 : 13

A takes 23 days = 10 units of ratio

So,  1 unit of ratio = 23/10

Time taken by B alone to finish the work = 23/10  ×13 = 29.9 = 30 days

Therefore, the No. of days taken to finish the work working together = 23 × 30/ 53

                                                                                              = 13 days. Ans.

Q. 54. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?

(a) 30 days   (b) 35 days    (c) 40 days    (d) 36 days   (e) None of these

Ans: (a) 30 days

Explanation:

That is , A = 3B/2/1/2 = 3B/2

Replacing A by 3B/2, we get

3B/2× B/3B/2 + B = 18 days

3 B ×B/5B =18

3B = 90

B = 30 days,  B alone can finish the work in 30 days. Ans.

Q. 55. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is:

(a) ¼    (b) 1/10    (c) 7/15     (d) 8/15    (e) None of these

Ans: (d) 8/15

Explanation:

Working together, the No. of days taken by them to finish the work = 15 × 20/35

                                                                             = 60/7 days.

Then, their 1 day’s work = 7/60

Their, 4 days work = 7 × 4/60 = 7/15 of the total work

Therefore, the fraction of the work, that is left = 1- 7/15 = 8/15. Ans.

Q. 56. A can finish a work in 18 days and B can do the work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work

(a) 5    (b) 5 ½    (c) 6    (d) 8    (e) None of these

Ans:  (c) 6 days

Explanation:

B’s one day’s work = 1/15

B’s 10 day’s work = 1/15 × 10 = 2/3

Remaining work = 1/3

A’s 1 day work = 1/18

No. of days A take to finish 1/3 of the work = 1/3/1/18 = 1/3 × 18 = 6 days. Ans.

Q. 57. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:

(a) 8 days   (b) 10 days   (c) 12 days   (d) 15 days   (e) None of  these

Ans:  (c) 12 days

Explanation:

No. of days taken by them working together = 15 × 10/25 = 6 days

Their 1 day’s work  = 1/6

Their 2 day’s work = 1/6 × 2 = 1/3

The work remaining = 2/3

A’s 1 day work = 1/15

Time taken by A to finish 1/3  of the work = 2/3/1/15 = 2/3 ×15 = 10 days

Therefore, the total number of days taken to finish the whole work = 10 +2 = 12 days. Ans.

Q. 58.  A can finish  a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

(a) 5 days   (b) 6 days   (c) 10 days    (d) 10 ½ days    (e) None of these

Ans: (c) 10 days

Explanation:

No. of days taken by B and C together to finish the work = 9 × 12/21 = 36/7 days

Their 1 day work = 7/36

So, their 3 day’s work = 7/36 × 3 = 7/12

The remaining work = 5/12

A’s 1 day’s work = 1/24

To finish the remaining 5/12 of the work, the No. of days taken by A = 5/12/1/24

                                                                                    = 5/12 ×24= 10 days. Ans.

Q. 59. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines  are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

(a) 11: 30 a.m.    (b) 12 noon    (c) 12:30 p.m.    (d) 1 p.m.  (e) None of these

Ans: (d) 1 p.m.

Explanation:

The three machines 1 hour’s work = 1/8 + 1/10 + 1/12 = 37/120

Their, work from 9 a.m. to 11 a.m. = 2 hour’s work = 37/120 × 2= 27/60

The remaining work = 23/60

Machines Q and R’s 1 hours work = 1/10 + 1/12 = 11/60

Therefore, the time taken by Q and R to finish the remaining 23/60 work = 23/60/11/60

                                                             = 23/60 × 60/11 = 23/11 = 2 hours approx.

Therefore, the approximate time at which the  work is finished = 11 + 2 = 1 p.m. Ans.

Q. 60. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish work?

(a) 18 days   (b) 24 days     (c) 30 days     (d) 36 days    (e) None of these

Ans: (a) 18 days

Explanation:

i.e. 2 ( A + B + C) ‘s 1 day’s work = 1/30 + 1/24 + 1/20 = 1/8

their 1 day’s work = 1/8/2 = 1/16

their 10 days work = 1/16 × 10 = 5/8

the remaining work = 3/8

A’s 1 day’s work = 1/16 – 1/24 = 1/48

Therefore, the No. of days A alone will take to complete 3/8 of the work = 3/8/ 1/48

                                  = 3/8 × 48 = 3 × 6 = 18 days. Ans.

Q. 61. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

(a) 6 days    (b) 10 days    (c) 15 days     (d) 20 days    (e) None of these

Ans: (b) 10 days

Explanation:

X’s 1 day’s work = 1/20

X’s 4 day’s work = 1/20 × 4 = 1/5

The remaining work = 4/5

X and Y’s 1 day work = 1/20 + 1/12 = 4/30 = 2/15

Therefore, Both together finish the remaining work in 4/5/2/15 days

                                              = 4/5 × 15/2 = 6 days

Therefore, the total number of days taken to finish the work = 4 + 6 = 10 days. Ans.

Q. 62. A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished he remaining work. In how many days A alone can finish the job?

(a) 40    (b) 50     (c) 54    (d) 60     (e) None of these

Ans: (d) 60

Explanation:

A + B ‘s 1 day’s work = 1/30

Their 20 day’s work = 1/30 × 20 = 2/3

Remaining work = 1/3

1/3 of the work is done by A in 20 days.

Then, whole work can be done by A in 3 × 20 = 60 days. Ans.

Q. 63. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

(a) 13 1/3 days    (b) 15 days    (c) 20 days    (d) 56 days    (e) None of these

Ans: (a) 13 1/3 days

Explanation:

A’s 8 day’s work = 1/40 × 8 = 1/5

Remaining work = 4/5

4/5 of the work is finished by Y in 16 days’

So, Y can finish the whole work alone in 16 ×5/4 days = 20days

They both together can finish it in 40 × 20/60 =13 1/3 days. Ans.

Q. 64.  A does 4/5 of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

(a) 23 days    (b) 37 days   (c) 37 ½ days    (d) 40 days   (e) None of these

Ans:  (c) 37 ½ days

Explanation:

A alone can finish the work in  20 × 5/4 days = 25 days

A’s 1 day’s work = 1/25

A and B together can finish the whole work in 5 × 3 days = 15 days

Their 1 day’s work = 1/15

Therefore, B’s 1 day’s work = 1/15 – 1/25 = 1/37 ½

Therefore, B alone can finish the whole work in 37 ½ days.Ans.

Q. 65. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

(a) 30 days    (b) 40 days     (c) 60 days    (d) 70 days   (e) None of these

Ans: (c) 60 days

Explanation:

A + B’s 1 day’s work = 1/30

i.e. A + B = 1/30    --------- (i)

16 A + 44 B = 1   ------ (ii)  ( i.e. 1 = the whole work done)

Multiplying (i) by 16 and subtracting it from (ii), we get

i.e. 16 A + 44 B = 1

      16 A + 16B = 8/15

                  28 B =7/15

B = 1/60 i.e. B’s 1 day’s work = 1/60

Therefore,  B alone can finish the work in 60 days. Ans.

Q. 66. A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?

(a) 16   (b) 24    (c) 36    (d) 48     (e) None of these

Ans: (b) 24

Explanation:

According to the question,

A + B’s 1 day’s work = 1/12

B+ C’s 1 days’ work = 1/16

A worked for 5 days, B for 7 days and C for 13 days. So, we can assume that,

A+ B has been working for 5 days and B+ C has been working for 2 days and C alone for 11 days.

i.e. A’s 5 day’s work + B’s 7 day’s work + C’s 13 day’s work = 1

(A+ B)’s 5 days work + (B + C)’s 2 days work + C’s 11 day’s work = 1

5/12 + 2/16 + C’s 11 days work = 1

So, C’s 11 day’s work = 1 – (5/12 + 2/16) = 11/24

C’s 1 days’ work = 11/24/11 = 1/24

Therefore, C alone can finish the work in 24 days. Ans.

Q. 67. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

(a) 6    (b) 8    (c) 9    (d) 12    (e) None of these

Ans: (c) 9

Explanation:

A and B together can finish the work in 45 × 40/85 = 360/17 days

A and B’s 1 day’s work = 17/360

A’s 1 day’s work = 1/45

B’s 1 day’s work = 1/40

B’s 23 day’s work 1/40 × 23 = 23/40

Remaining work = 1 – 23/40 = 17/40

17/40 of the work is done by A and B together

17/40 of the work is done by A and B together in = 17/40/17/360 = 17/40 × 360/17 days

                                                            = 9 days.

Therefore, A left after 9 days. Ans.

Q. 68. A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in:

(a) 3 days   (b) 5 days   (c) 7 days   (d) 11 days   (e) None of these

Ans: (b) 5 days

Explanation:

A’ s 1 day’s work = 1/20

B’s 1 day’s work = 1/12

B’s 9 days work = 1/12 × 9 = ¾

Remaining work = ¼

A can finish the remaining work in = 1/4/1/20 = ¼ ×20 = 5 days. Ans.

Q. 69. A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in

(a) 5 days   (b) 6 days    (c) 9 days    (d) 10 days   (e) None of these

Ans: (b) 6 days

Explanation:

A and B’s 1 day’s work = 1/3

Their 2 day’s work = 1/3 × 2 = 2/3

Remaining work = 1/3

1/3 of the work is finished by A in 2 days

Then, the whole work can be finished by A alone in 3 × 2 = 6 days

So, A’s 1 day’s work = 1/6

Therefore, B’s 1 day’s  work = 1/3 – 1/6 = 1/6

Therefore, the whole work can be done B alone in 6 days. Ans.

Q. 70. A man, a woman and a boy together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?

(a) 9 days   (b) 21 days   (c) 24 days    (d) 27 days   (e) None of these

Ans: (a) 9 days

Explanation:

(Man + Boy + Woman)’s 1 day’s work = 1/3

Man’s 1day’s work = 1/6

Boy’s 1 day’s work = 1/18

Then, Woman’ 1 day’s work = 1/3 – ( 1/6 + 1/18) = 1/3 – 4/18 =2/18 = 1/9

Therefore, the Woman alone can finish the work in 9 days. Ans.

Q. 71. A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the work?

(a) 7 ¾    (b) 8 4/5     (c) 9 3/8      (d) 10    (e) None of these

Ans: (c) 9 3/8

Explanation:

A can do finish the whole work in 3 × 5 days = 15 days

B can finish the whole work in 5 /2 × 10 days = 25 days

A and B together can finish the work in 15 × 25/ 40 days = 9 3/8 days. Ans.

Q. 72. A and B can do a piece of work in 12 days; B and C can do it in 15 days and C and A can do it in 20 days. A alone can do the work in:

(a) 15 2/3 days   (b) 24 days   (c) 30 days    (d) 40 days     (e) None of these

Ans: (c) 30 days

Explanation:

2 (A + B + c)’s 1 day’s work = 1/12 + 1/15 + 1/20 = 12/60 = 1/5

A + B + C’s 1 day’s work = 1/5/2 = 1/10

A’s 1 day’s work = 1/10 – (B + C)’s 1 day’s work = 1/10 – 1/15 = 1/30

Therefore, A alone can finish the work in 30 days. Ans.

Q. 73. A and B together can complete a piece of work in 8 days while B and C together can do it in 12 days. All the three together can complete the work in 6 days. In how much time will A and C together complete the work?

(a) 8 days   (b) 10 days   (c) 12 days    (d) 20 days    (e) None of these

Ans: (a) 8 days

Explanation:

A’s 1 day’s work = A + B + C’s 1 day’s work – B + C’s 1 day’s work = 1/6 – 1/12

                                                                                     = 1/12

B’s 1 day’s work = A + B’s 1 day’s work – A’s 1 day’s work = 1/8 – 1/12= 1/24

C’s 1 day’s work = B+ C’s 1 day’s work – B’s 1 day’s work = 1/12 – 1/24 = 1/24

A +B’ 1 day’s work = 1/12 + 1/24 = 3/24

Therefore, A and C together will finish the whole work in 24/3 = 8 days. Ans.

Q. 74. A can do a work in 4 days, B can do it in 5 days and C can do it in 10 days. A, B and C together can do the work in

(a)  1 3/5 days    (b) 1 9/11 days   (c) 2 5/6 days    (d) 3 days    (e) None of these

Ans: (b) 1 9/11 days

Explanation:

When A, B and C can do a work in x, y and z days respectively. Then, the three of them together can finish the work in  xyz/ x y + y z + x z  days

That is, A, B and C together ca do the work in 4 × 5 × 10/ 20 + 50 + 40

                                                                = 4 × 5 × 10/110 = 20/11 = 1 9/11 days. Ans.

Q. 75. 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?

(a) 4 days   (b) 10 days    (c) 15 days    (d) 20 days   (e) None of these

Ans: (a) 4 days

Explanation:

3 men = 5 women

1 woman = 3/5 men

So, 5 women = 3/5 × 5 = 3 men

6 men and 5 women = 6 + 3 = 9 men

1 work done = 3 men × 12 days

3 × 12 = 9 × ? days

? days = 3 × 12/9 = 4 days. Ans.

Q. 76. Kamal can do a work in 15 days. Bimal is 50% more efficient than Kamal. The number of days, Bimal will take to do the same piece of work, is

(a) 10     (b) 10 ½     (c) 12    (d) 14    (e) None of these

Ans: (a) 10

Explanation:

Kamal’s 15 days is 150% of No. days taken by Bimal to finish the job.

Therefore, the No. of days taken by Bimal = 15/150 × 100 = 10 days. Ans.

Q. 77. A does 20% less work than B. if A can complete a piece of work in 7 ½ hours, then B can do it in

(a) 5 hours   (b) 5 ½ hours    (c) 6 hours   (d) 6 ½ hours    (e) None of these

Ans: (c) 6 hours

Explanation:

B can finish the work in 80% of 7 ½ hours of time

7 ½ = 15/2

Therefore, time taken by B = .8 × 15/2 = 30/5 = 6 hours. Ans.

Q. 78. Ram and Shyam together  can finish a job in 8 days. Ram can do the same job on his own in 12 days. How long will Shyam take to do the job by himself?

(a) 16 days   (b) 20 days    (c) 24 days    (d) 30 days    (e) None of these

Ans:  (c) 24 days

Explanation:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.

Therefore,  the No. of days Shyam take to finish the job alone = 8 × 12/12 – 8

                                                                          = 8 × 12/4 = 24 days. Ans.

Q. 79. The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio:

(a) 3 : 4   (b) 9 : 16    (c) 4 : 3    (d) 3 : 2    (e ) None of these

Ans: (c) 4 : 3

Explanation:

The No. of days taken by them = inverse ratio = 4 : 3. Ans.

Q. 80. A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there?

(a) 30    (b) 40   (c) 32    (d) 36    (e) None of these

Ans:  (b) 40

Explanation:

Let ‘x’ be the original number of men

Then 1 work done = x × 60

Then, 60x = (x + 8) 50

 60x = 50x + 400

10 x = 400

x = 40. Ans.

Q. 81. A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?

(a) 30 days    (b) 35 days   (c) 40 days    (d) 42 days   (e) None of these

Ans: (a) 30 days

Explanation:

Let ‘x’ be the number of days taken by B alone to finish the whole work

Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days.

Then, working together,

               3x/2 × x/3x/2 + x = 18 days

               3x × x/5x = 18

               3x/5 = 18

             Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days. Ans.

Q. 82. A and B can finish a piece of work in 12 days and 18 days respectively. A begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in

(a) 14 1/3 days   (b) 15 2/3 days   (c) 16 1/3 days   (d) 18 2/3 days   (e) None of these

Ans: (a) 14 1/3 days

Explanation:

Both of them together can finish the work (daily working) in 12 × 18/30 days = 36/5

                                                                                                              = 7 1/5 days.

By working in alternate days, their 2 day’s work = 5/36

Their, 14 day’s work (because they take more than double of 7 days) = 5/36 × 7

                                                                                           = 35/36

Remaining work = 1 – 35/36 = 1/36

Because A started the work, the remaining work is finished by A

A’s 1 day’s work = 1/12

Therefore, the No. of days taken by A to finish 1/36 work = 1/36/1/12 = 1/3 days.

Therefore, the total work is completed in 14 + 1/3 = 14 1/3 days. Ans.

Q. 83. A can do a piece of work in 14 days which B alone can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days for the work to be completed is

(a) 6 3/5 days    (b) 8 ½ days      (c) 10 1/5 days   (d) 13 ½ days    (e) None of these

Ans: (c) 10 1/5 days

Explanation:

B’s 1 day’s work = 1/21

B’s 3 day’s work = 1/21 ×3 = 1/7

The remaining work finished by both of them = 1 – 1/7 = 6/7

Both together can finish it in 14 × 21/35 days = 42/5 days

Their, 1 day’s work = 5/42

Therefore, the No. of days taken by them together to finish 6/7 work

                                                  = 6/7/5/42 = 6/7 × 42/5 =  36/5 = 7 1/5 days

Therefore, the total No. of days for the work to be completed = 3 + 7 1/5 = 10 1/5 days. Ans.

Q. 84. A and B can finish a piece of work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. A alone can finish the work in

(a) 48 days    (b) 50 days    (c) 54 days     (d) 60 days   (e) None of these

Ans:  (d) 60 days

Explanation:

(A + B)’s 1 day’s work = 1/30

Their 20day’s work = 1/30 × 20 = 2/3

Remaining 1/3 work is done by A in 20 days

Therefore, A alone can finish the work in 3 × 20 = 60 days. Ans.

Q. 85. 10 women can complete a work in 8 days and 10 children take 12 days to complete the work. How many days will 6 women and 3 children together take to complete the work?

(a) 7    (b) 8     (c) 9    (d) 12     (e) None of these

Ans: (e) None of these

Explanation:

1 women’s 1 day’s work = 1/8/10 = 1/80

1 child’s 1 day’s work = 1/12/10 = 1/120

6 women’s 1 day’s work = 1/80 × 6 = 3/40

3 children’s 1 day’s work = 1/120 × 3 = 1/40

6 women’s + 3 children’s 1 day’s work = 3 /40 + 1/40 = 1/10

Therefore, they will finish the whole work in 10 days. Ans.

Q. 86. 9 children can complete a piece of work in 360 days; 18 men can complete the same piece of work in 72 days and 12 women can complete it in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?

(a) 68 days   (b) 81 days   (c) 96 days   (d) 124 days   (e) None of these

Ans:  (b) 81 days

Explanation:

1 child’s 1 day’s work = 1/360 ×9 = 1/3240

10 children’s 1 day’s work = 1/324

1 man’s 1 day’s work = 1/72 × 18 = 1/1296

4 men’s 1 day’s work = 1 ×4/1296 = 1/324

12 women’s 1 day’s work = 1/162  given

Then, (4 men + 12 women + 10 children)’s 1 day’s work = 1/324 + 1/162 + 1/324

                     = 1/324 + 2/324 + 1/324 = 4/324 = 1/81

Therefore, the required No. of days = 81 days. Ans.

Q. 87. 9 men working 7 hours a day can complete a piece of work in 15 days. How many days can 6 men working for 9 hours a day, complete the same piece of work?

(a) 15 ¾ days    (b) 16 days    (c) 16 ¾ days    (d) 17 ½ days    (e) None of these

Ans: (d) 17 ½ days

Explanation:

1 work done = 9 × 7 × 15

9 × 7 × 15 = 6 × 9 × ? days

? days = 9 × 7 × 15/6 × 9

           = 35/2 = 17 ½ days. Ans.

Q. 88. A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?

(a) 9 days   (b0 21 days   (c) 24 days   (d) 27 days   (e) None of these

Ans: (a) 9 days

Explanation:

(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3

1 man’s 1 day work = 1/6

  1boy’s 1 day’s work = 1/18

(1 Man + 1 boy) ‘s 1 day’s work =  1/6 + 1/18 = 2/9

 Therefore, 1 woman’s 1 day’s work = 1/3 – 2/9 = 3-2/9 = 1/9

Therefore, the woman alone can finish the work in 9 days. Ans.

Q. 89. 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 10 children together complete the piece of work?

 (a) 5 days    (b) 15 days    (c) 28 days     (d) 6 days     (e) None of these

Ans: (d) 6 days

Explanation:

1 man’s 1 day’s work = 1/8 × 12 = 1/96

10 men’s 1 day’s work = 1 × 10/96  = 5/48

1 woman’s 1 day’s work = 1/192

4 women’s 1 day’s work = 1/192 × 4 = 1/48

1 child’s 1 day’s work = 1/240

10 children’s 1 day’s work = 1/24

Therefore, (10 men + 4 women + 10 children)’s 1 day’s work = 5/48 + 1/48 + 1/24

                                          = 8/48 =1/6

The required No. of days = 6 days. Ans.

Q. 90. 8 men can dig a pit in 20 days. If a man works half as much again a s a boy, then 4 men and 9 boys can dig a similar pit in:

(a) 10 days   (b) 12 days      (c) 15 days     (d) 16 days    (e) None of these

Ans:  (d) 16 days

Explanation:

1 work done = 8 × 20

1 man = 3/2 Boys

1 boy = 2/3 men

Then, 9 boys = 9 × 2/3 men = 6 men

Then, 4 men + 9 boys = 10 men

Then, 8 × 20 = 10 × ?days

? days = 8 × 20/10 = 16 days. Ans.

Q. 91. A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?

(a) 72 days     (b) 20 days    (c) 24 days     (d) 36 days    (e) None of these

Ans: (a) 72 days

Explanation:

(man + boy)’s 1 day’s work = 1/24

Their 20 day’s work = 1/24 × 20 = 5/6

The remaining 1/6 work is done by the man in 6days

Therefore, the man alone will finish the work in 6 × 6 days = 36 days

Man’s 1 day’s work = 1/36

Therefore, boy’s 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72

Therefore, the Boy alone will finish the work in 72 days. Ans.

Q. 92. A, B and C completed a piece of work costing Rs.1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio 5 : 6 : 4, how much amount will be received by A?

(a) Rs.800    (b) Rs. 600   (c) Rs.900    (d) Rs.750    (e) None of these

Ans: (b) Rs. 600

Explanation:

           The new ratio = wages ratio × No. of days

A = 5 × 6 = 30

B = 6 × 4 = 24

C = 4 × 9 = 36

Therefore, the ratio of the amount received = 30 : 24 : 36 = 5 : 4 :6

Total ratio = 15

1 unit of ratio = 1800/15 = Rs. 120

 Therefore, amount received by A = 5 units = 5 × 120 = Rs.600. Ans.

Q. 93. 12 men take 36 days to do a work while 12 women complete 3/4^th of the same work in 36 days. In how many days 10 men and 8 women together will complete the same work?

(a) 6 days   (b) 12 days    (c) 27 days    (d) Data inadequate   (e) None of these

Ans: (c) 27 days

Explanation:

1 man’s 1 day’s work = 1/ 36 × 12 = 1/432

10 men’s 1 day’s work = 10/432

12 women can finish the whole work in 4 × 36/3 = 48 days

1 woman’s 1 days work = 1/ 48 × 12 = 1/576

8 women’s 1 day’s work = 8/572 = 1/72

(10 men + 8 women)’s 1 day’s work = 10/432 + 1/72 = 10 + 6/432 = 16/432

                                                   = 1/27

Therefore, the required No. of days = 27 days. Ans.

Q. 94. A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. working together, they can do it in

(a) 20 days   (b) 22 ½ days   (c) 25 days    (d) 30 days   (e) None of these

Ans: (b) 22 ½ days

Explanation:

B = 3A

3A – A =60 days

A = 30days

Then, B = 90 days

(A + B) = 30 × 90/ 120 = 45/2 = 22 ½ days . Ans.

Q. 95. A works twice as fast as B. if both of them can together finish a piece of work in 12 days, then B alone can do it in

(a) 24 days   (b) 27 days    (c) 36 days    (d) 48 days     (e) None of these

Ans: (c) 36 days

Explanation:

B = 2A

2A × A/3A = 12

2A/3 = 12

A = 18 days

B  = 2 × 18 = 36 days

Therefore, B alone can finish the work in 36 days. Ans.

Q. 96. A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the  job in 1/4^th of a day?

(a) 10  (b) 14   (c) 19    (d) 41   (e) None of these

Ans: (d) 41

Explanation:

1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12

1 woman’s 1 day’s work = ¼,    ¼ day’s work = ¼ × ¼ = 1/16

1 boy’s 1 day’s work = 1/12,     ¼ day’s work = 1/12 × ¼ = 1/48

Let ‘x’ be the No. of boys required.

Then, (1 man + 1 woman + x boy)’s ¼ day’s work   1/12 + 1/16 + x/48 = 1

                                                                    = 4 + 3 + x       = 1

                                                                           48

                                             i.e. 7 + x= 48  and  x = 41. Ans.

Q. 97. A does 4/5^th of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

(a) 23 days    (b) 37 days   (c) 37 ½ days   (d) 40 days   (e) None of these

Ans:  (c) 37 ½ days

Explanation:

A can finish the whole work in 20 × 5/4 days = 25 days

A and B together finish the whole work in 5 × 3 days = 15 days

Therefore, B can finish the whole work in  25 B/ 25 + B = 15

      25 B = 15 ( 25 + B)= 375 + 15B

10B = 375 and B = 375/10 = 37 ½ days. Ans.

Q. 98.  A can do 1/4^th part of the work in 10 days, B can do 40% of the work in 40 days and C can do 1/3^rd of the work in 13 days. Who will complete the work first?

(a) A    (b) B    (c) C    (d) A and C both   (e) None of these

Ans: (c) C

Explanation:

The whole work is done by A in 4 × 10 = 40 days

B can do the whole work in 40/40 × 100 days = 100 days

C can do the whole work in 3 × 13 = 39 days.

Therefore, the 1^st person to complete the work is C. Ans.

Q. 99. A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get:

(a) Rs.1200   (b) Rs.1500   (c) Rs. 1800    (d) Rs.2000   (e) None of these

Ans: (c) Rs.  1800

Explanation:

Ratio of working days of A : B = 10 : 15

Therefore, their wages ratio = reverse ratio = 15 : 10

 Therefore, A will get 15 units of ratio

Total ratio = 25

1 unit of ratio =3000/25 = 120

So, A’s amount = 120 × 15 = Rs.1800. Ans.     

Q. 100. Directions:   (Questions 1 to 5):

             Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is /are necessary to answer the question.

1.      In how many days can A and B working together complete a job?     

I.                   A alone can complete the job in 30 days.

II.                B alone can complete the job in 40 days

III.             B takes 10 days more than A to complete the job.

(a)    I and II only  (b) II and III only    (c) I and III only  (d) Any two of the three (e) All I , II and III

2.      In how many days can the work be completed by A and B together ?

I.                   A alone can complete the work in 8 days.

II.                If A alone works for 5 days and B alone works for 6 days, the work gets completed.

III.             B alone can complete the work in 16 days.

(a)    I and II only   (b) II and III only     (c) Any two of the three   (d) II and either I or III     (e) None of these

3.      How many workers are required to complete the construction work in 10 days?

I.                   20% of the work can be completed by 8 workers in 8 days.

II.                20 workers can complete the work in 16 days.

III.             One-eighth of the work can be completed by 8 workers in 5 days.

(a)    I only   (b) II and III only   (c) III only (d) I and III only (e ) Any one of the three.

4.      In how many days can the work be done by 9 men and 15 women?

I.                   6 men and 5 women can complete the work in 6 days.

II.                3 men and 4 women can complete the work in 10 days.

III.             18 men and 15 women can complete the work in 2 days.

(a)    III only    (b) All I, II and III    (c) Any two of the three    (d) Any one of  the three   (e) None of these

5.      In how many days can 10 women finish the work?

I.                   10 men can complete the work in 6days

II.                10 men and 10 women together can complete the work in 3 3/7 days.

III.             If 10 men work for 3 days and thereafter 10 women replace them, the remaining work is completed in 4 days.

(a)    Any two of the three   (b) I and II only    (c) II and III only  (d) I and III only (e) None of these

       Answers with explanations:

1.      Ans: (d)  Any two of the three

Explanation:

I.                   A’s 1day’s work = 1/30

II.                B’s 1 day’s work = 1/40

III.             B’s 1 day’s work = 1/40

I and II gives the answer,

I and III gives the answer,

II and III gives the answer,

Therefore, the correct answer is (d). Ans.

2.      Ans: (c) Any two of the three

Explanation:

I.                   A’s 1 day’s work = 1/8

II.                1 work done = A’s 5 days work + B’s 6 day’s work

III.             B’s 1 day’s work = 1/16

So, I and II gives the answer,

      I and III gives the answer,

      II and III gives the answer.

Therefore, the correct answer is (c) .Ans.

3.      Ans: (e) Any one of the three

Explanation:

I.                   1 worker’s 1 day’s work = 1/320, required No. of workers = 320/10 =32.

II.                1 worker’s 1 day’s work = 1/320

III.             1 worker’s 1 day’s work = 1/320

Therefore, I alone gives the answer

                II alone gives the answer

                III alone gives the answer

Therefore, the correct answer is (e). Ans.

4.      Ans: (c) Any two of the three

Explanation:

I.                   Gives, the linear equation 6x + 5y = 6

II.                Gives, the linear equation 3x + 4 y = 10

III.             Gives, the linear equation 18x + 15 y = 2

i.e. Any two of the equations gives the correct answer.

Therefore, the correct answer is (c) Ans.

5.      Ans: (b) I and II only

Explanation:

I.                   Gives, 1 man’s 1 day’s work = 1/60

II.                I and II gives 1 woman’s 1 day’s work = 1/80

III.             (10 men + 10 women)’s 1 day’s work = 1/7

Therefore, I and II gives the answer

So, the correct answer is (b). Ans.       

Solution to Mitul Sharma's Question on Time and Work

 Question: A certain work can be done in a certain time by 25 men. With 5 men less it could have been done in 3 days more. In what time can it be done by 40 men. 
 Solution:
 let x be the time taken by 25 men to complete the work in days.
Then, 25 * x   = 20 * (x + 3)
          25x = 20x + 60
          x = 12
Then, 40 men will compete the work in  = 25 * 12/40 = 15/2 = 7 1/2 days.