Problems on Age

Problems on Ages

Q. 1. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is:

(a) 1 year   (b) 2 years   (c) 3 years   (d) 5 years   (e) None of these

Ans: (c) 3 years

Explanation:

Now, Sum of the ages of the 4 members = 4 ×24 + 4 × 10 = 136 years

Let ‘x + 2” and ‘x’ be the ages of the new born elder and younger children respectively.

Then the present average,  136 + x +2 +  x/6 = 24

 2x = 24 × 6 – 138 = 144 – 138 = 6

Therefore, x = 3 years. Ans.

Q.2.  3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is

(a) 1 year    (b) 1 ½ years    (c) 2 years    (d) 3 years    (e) None of these

Ans: (c) 2 years

Explanation:

Present Sum of the ages of 5 members = 5 × 17 + 5 × 3 = 100

Including the new born baby’s age as ‘x’, the present average  100 + x/6 =  17

     Then, x = 102 -100 = 2 years. Ans.

Q.3.  The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

(a) 35 years   (b) 40 years   (c) 50 years     (d) 34 years   (e) None of these

Ans: (b) 40 years

Explanation:

Sum of the present ages of Husband, wife and child = 27 × 3 + 3 × 3= 90

Sum of the present ages of wife and child = 2 × 20 + 2 × 5 = 50 years

Therefore, the present age of husband = 90 – 50 = 40 years. Ans.

Q. 4.  Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?

(a) 24 years   (b) 27 years   (c) 28 years   (d) 30 years   (e) None o f these

Ans:  ( a) 24 years

Explanation:

Sum of present ages of A and B = 2  × 18 + 2 × 3 = 42 years

The new average i.e. 42 + C/ 3 = 22

C = 22 × 3 – 42 = 66 – 42 = 24 years. Ans.

Q. 5. The average age of a husband and wife was 23 years at the time of their marriage. After five years they have a one- year old child. The average age of the family now is:

(a) 19 years   (b) 23 years   (c) 28.5 years     (d) 29.3 years    (e) None of these

Ans: (a) 19 years

Explanation:

The present average age of the family = 23 × 2 + 2× 5 + 1/3 = 57/3 = 19 .Ans.

Q. 6. A family consists of grandparents, parents and three children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

(a) 28 4/7 years   (b) 31 5/7 years    (c) 32 1/7 years   (d) 31 years  (e) None of these

Ans: (b) 31  5/7 years

Explanation:

Sum of the ages of grandparents = 2 × 67 = 134

Sum of the ages of parents = 2 × 35 = 70

Sum of the ages of children = 3 × 6 = 18

Therefore, the average age of the family = 134 + 70 + 18/7 = 222/7 = 31 5/7 years. Ans.

Q. 7. The average age of three boys is 16 years. If their ages are in the ratio 4 : 5 : 7, then the age of youngest boy is :

(a) 8 years    (b) 9 years   (c) 12 years    (d) 16 years   (e) None of these

Ans: (c) 12 years

Explanation:

Sum of their ages = 3 × 16 = 48

Sum of ratio = 4 + 5 + 7 = 16

1 unit of ratio = 48/16 = 3

Therefore, the age of  the youngest boy = 4 × 3 = 12 years. Ans.

Q. 8. Average age of 6 sons of a family is 8 years. Average age of the sons together with their parents is 22 years. If the father is older than the mother by 8 years, then the age of the mother is

(a) 44 years   (b) 52 years   (c) 60 years    (d) 68 years    (e) None of these

Ans: (c) 60 years

Explanation:

Sum of the ages of 6 sons = 6 × 8 = 48

Sum of the ages of 6 sons  and their  parents = 8 × 22 = 176

Therefore, the sum of the ages of their parents = 176 – 48 = 128

The age of the mother = 128 -8/2 = 60 years. Ans.

Q. 9. The average age of the mother and her six children is 12 years which is reduced by 5 years if the mother is excluded. How old is the mother?

(a) 40 years   (b) 42 years   (c) 48 years   (d) 50 years   (e) None of these

Ans:  (b) 42 years

Explanation:

Sum of the ages of 6 children and their mother = 7 × 12 = 84

Sum of the ages of 6 children = 6 × 7 = 42

Therefore, the age of the mother = 84 – 42 = 42 years. Ans.

Q. 10. The average age of A, B and C is 7 years. The average age of A and B is 6 years and that of B and C is 8 years. Find the age of B.

(a) 6 years    (b) 7 years     (c) 8 years   (d) 9 years    (e) None of these

Ans: (b) 7 years

Explanation:

The Sum of the ages of A , B and C = 21

The sum of ages of A and B = 12

Sum of the ages of B and C = 8

Therefore, age of A = 21 -  16 = 5

Therefore, the age of B = 12 – 5 = 7 years. Ans.

Q. 11. The average age of 3 friends is 23. Even if the age of the 4^th friend is added, the average remains 23. What is the age of the 4^th friend?

(a) 21 years   (b) 23 years     (c) 32 years    (d) Cannot be determined   (e) None of these

Ans: (b) 23 years

Explanation:

Sum of the ages of 3 friends = 3 × 23 = 69

That of the 4 friends = 4 × 23 = 92

Therefore, the age of 4^th friend = 92 – 69 = 23 years. Ans.

Q. 12. The average age of a husband and wife was 23 years when they were married 5 years ago. The average age of the husband, the wife and a child who was born during the interval, is 20 years now. How old is the child now?

(a) Less than 1 year  (b) 1 year    (c) 3 years    (d) 4 years   (e) None of these

Ans: (d) 4 years

Explanation:

Sum of present ages of husband and wife = 2 × 23 + 2 × 5 = 46 + 10 = 56

Sum of the present ages of husband, wife and the child = 3 × 20 =60

Therefore, the age of the child = 60 – 56 = 4 years. Ans.

Q. 13. Three years ago the average age of A and B was 18 years. With C joining them now, the average becomes 22 years. How old is she now?

(a) 24 years   (b) 27 years  (c) 28 years     (d) 30 years   (e) None of these

Ans: (a) 24 years

Explanation:

The sum of present ages of A and B = 2 × 18 + 2 × 3 = 36 + 6 = 42

The sum of present ages of A, B and C = 3 × 22 = 66

Therefore, the age of  C = 66 – 42 = 24 years. Ans.

Q. 14. The average age of a husband and wife was 23 years at the time of their marriage. After five years they have a one year old child. The average age of  the family now is

(a) 28.5 years    (b) 19 years    (c) 29.3 years     (d) 23 years    (e) None of these

Ans:   (b) 19 years

Explanation:

Sum of the present ages of the family = 2 × 23 + 2 × 5 + 1 = 57

Therefore, the average age of the family = 57/3 = 19 years. Ans.

Q. 15. At present the sum of ages of R and K is 63 years. The ratio of their ages after 7 years will be 7 : 4. What is the present age of R?

(a) 40 years   (b) 42 years    (c) 38 years    (d) 39.5 years    (e) None of these

Ans:  (b) 42 years

Explanation:

After 7 years sum of their ages = 63 + 14 = 77

Sum of the ratio = 11

So,, 1 unit of ratio = 77/11 = 7

Therefore, the present age of R = 7 × 7 – 7 = 49 – 7 = 42 years. Ans.

Q. 16. The ages of K and C are in the ratio 3 : 7.  After 2 years their age will be in the ratio 1 : 2. The sum of their ages is

(a) 18 years   (b) 20 yeas  (c) 37 years    (d) 50 years     (e) None of these

Ans: (b) 20 years

Explanation:

Let the ages of K and C be 3x and 7x respectively

Then, 3x + 2/7x + 2 = ½

2 ( 3x + 2) = 7x + 2

6x + 4 = 7x + 2  so, x = 2

Sum of their ages = 3x + 7x = 3 × 2 + 7 × 2 = 6 + 14 = 20 years. Ans.

Q. 17. Ratio of A’s to P’s age is equal to 4 : 3. A will be 26 years old after 6 years. How old is P now?

(a) 12 years   (b) 21 years   (c) 15 years    (d) 19 ½ years    (e) None of these

Ans: (c) 15 years

Explanation:

A’s present age = 26 – 6 = 20 years

20 is 4 units of ratio. And 1 unit of ratio = 5

Therefore, P’s age = 3 units of ratio = 3 × 5 = 15 years. Ans.

Q. 18. 10 years ago A’s mother was 4 times older than her daughter. After 10 years the mother will be two times the age of her daughter. The present age of A is

(a) 5 years    (b) 10 years    (c) 20 years    (d) 30 years    (e) None of these

Ans:  (c) 20 years

Explanation:

Let ‘x’ be the present age of the daughter and ‘y’ that of the mother

Then, y – 10 = 4 ( x – 10)

         y – 10 = 4x – 40

4x – y = 30 ------(i)

And    y + 10 = 2 ( x + 10)

y + 10 = 2x + 20

2x –y = 10 – 20

2x – y = -10 ------ (ii)

Subtracting (ii) from (i)

We get, x =  20.

Therefore, the present age of the daughter (A) = 20 years. Ans.

Q. 19. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is

(a) 29 years   (b) 39 years    (c) 19 years    (d) 49 years   (e) None of these

Ans:  (b) 39 years

Explanation:

Let the present ages of A and B are ‘x’ and ‘y’ years respectively,

Then, x + 10 = 2 (y – 10) =2y – 20

x – 2y = -30  ---------(i)

x – y = 9  ------ (ii)

solving (i) and (ii), we get, y = 39 years. Ans.

Q. 20. The ratio of the mother’s age to the daughter’s age is 4 : 1. The product of their ages is 196. The ratio of their ages after 8 years will be

(a) 8 : 3 (b) 12 : 5    (c) 5 : 3    (d) 7 : 3     (e) None of these

Ans: (b) 12 : 5

Explanation:

Let the present ages of the mother and her daughter are x and y respectively.

Then, x = 2y

x y = 196

i.e. 4 y ² = 196

y² =196/4 = 49

y = 7

then, x = 28

after 8 years their ages will be 36 and 15 respectively and the ratio = 12 : 5. Ans.

Q. 21. If  difference between ages of B and R is 15 years and ratio of their ages is 3 : 2, then the ages of R is

(a) 25 years   (b) 20 years   (c) 28 years (d) 30 years   (e) None of these

Ans:  (d) 30 years

Explanation:

Hence, the difference in ages is given,

Age of R =  R’s ratio/ difference in ratio × difference in age

               = 2 × 15/3-2 = 30 years. Ans.

OR

Let  x and y be the present  ages of B and R respectively

Then, x – y = 15

x/y =3/2

2x = 3y

x = 3y/2

3y /2 – y = 15

3y – 2y = 30

So, y = 30. Ans.

Q. 22. Ten years ago the ratio of ages of P and Q was 5 : 3. If the difference between their ages after 9 years will be 8 years. The present age of P is

(a) 30 years   (b) 25 years   (c) 16 years   (d) 28 years    (e)  None of these

Ans: (a) 30 years

Explanation: Hence, the difference in ages is given,

Age of P 10 years ago =  P’s ratio/ difference in ratio × difference in age

                                      = 5/5-3 × 8 = 5 × 4 = 20 years

Therefore, P’s present age = 20 +10 = 30 years. Ans.

Q. 23. The present age difference between father and son is 14 years. The ratio of their ages will be 4 : 3 after 11 years. How old is son now?

(a) 25 years    (b) 31 years   (c) 30 years     (d) 28 years    (e) None of these

Ans: (b) 31 years

Explanation:

Hence, the difference in ages is given,

Age of son after 11 years ago =  Son’s ratio/ difference in ratio × difference in age

                                                = 3 × 14/4-3 = 3 × 14 = 42 years

Therefore, the present age of son = 42 – 11 = 31 years. Ans.

Q. 24. The sum of the ages of husband and wife is 70 years and ratio of their ages is 3 : 2. The age of the wife is

(a) 32 years   (b) 25 years   (c) 28 years    (d) 27 years   (e) None of these

Ans:  (c) 28 years

Explanation:

Hence, the sum of ages is given,

Age of wife =  wife’s ratio/ sum of  ratio × sum of age

                    = 2 × 70/ 3 + 2 = 140/5 = 28 years. Ans.

Q. 25.  The ratio of present ages of x and y is 2 :3 and the sum of their ages after 4 years will be 68 years. What is the age of y now?

(a) 35 years   (b) 36 years   (c) 24 years   (d) 28 years   (e) None of these

Ans:  (b) 36 years

Explanation:

Hence, the sum of ages is given,

Sum of their present age = 68 – 8 = 60

Age of y =  y’s ratio/ sum of  ratio × sum of age

Therefore, the present age of y = 3 × 60/ 2 +3 = 3 × 60/5 = 3 × 12 = 36 years. Ans.

Q. 26. The average age of Rajan and Sajan after a period of 5 years from now will be 20 years. Rajan’s  present age is 12 years. What is their average age now?

(a) 14    (b) 15    (c) 10    (d) 17   (e) None of these

Ans: (b) 15

Explanation:

Sum of their ages after 5 years = 2 × 20 = 40

Sum of their present ages = 40 – ( 2 × 5) = 30 years.

Their average age now = 30/2 = 15. Ans.

Q. 27. The average age of P, Q and R is 5 years more than R’s age. If the total ages of P and Q together is 39 years, what is R’s age?

(a) 24 years   (b) 16 years    (c) 14 years    (d) 12 years   (e) None of these

Ans:  (d) 12 years.

Explanation:

P + Q + R = 3 ( 5 + R) = 3R + 15

R = 3R + 15 – 39

39 – 15 = 3R – R

 24 = 2R

Therefore, R’s age = 12 years. Ans.

Q. 28. The average age of A and B is 54 years, the average age of B and C is 55 years and the average age of C and A is 59 years. What is the age of B in years?

(a) 62    (b) 48    (c) 56     (d) 50    (e) None of these

Ans: (d) 50

Explanation:

A + B = 108, B +C = 110   and C + A = 118

Then, 2 (A + B + C) = 108 + 110 + 118 = 336

 (A + B + C) = 336/2 = 168

Age of B =  (A + B + C) – C + A = 168 – 118 = 50 years. Ans.

Q. 29. Five years ago average age of P and Q was 15 years. Average age of P, Q and R today is 20 years. How old R will be after 10 years?

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

Ans:  (c) 30 years

Explanation:

The sum of ages of P and Q 15 years ago = 2 × 15 = 30 years

The present average age of P and Q = 30 + 2 × 5 = 40 years

Sum of present ages of P , Q and R = 3 × 20 = 60 years

Present age of R = 60 -40 = 20 years

Therefore, the age of R after 10 years will be = 20 + 10 = 30 years. Ans.

Q. 30. The age of three members of a family are 5, 10, 15 years respectively. What is their average age?

(a) 10 years   (b) 5 years   (c) 15 years   (d) 20 years  (e) None of these

Ans: (a) 10 years

Explanation:

The average age = (5 + 10 + 15)/3 = 10 years. Ans.

Q.31. Ten years ago, the average age of a family of four members was 24 years. Three children having been born, the average age of the family is same today. What are the present ages of children, if two children are identical twins and differ by two years from the younger one?

(a) 12, 12, 10   (b) 8, 8, 6   (c) 13, 13, 11   (d) 14, 14, 12 (e) None of these

Ans: (e) None of these

Explanation:

Sum of the ages of four members 10 years ago = 4 × 24 = 96

Their present sum = 96 + 4 × 10 = 136

Sum of the present ages of the family including 3 recently born children = 7 × 24 = 168

Then, the sum of ages of 3 children = 168 – 136 = 38

Total difference between younger child and the twins = 4

Total sum excluding the difference = 38 – 4 = 34

Age of each child = 34/3 + 2, 34/3 + 2, 34/3

                             = 13 1/3, 13 1/3  , 11 1/3 respectively. Ans.

Q.32. The average age of a family of five persons is 20 years. If the youngest member is 8 years old. What was the average age of the family at the time of birth of the youngest member?

(a) 12 years  (b) 15 years    (c) 18 years    (d) 16 years    (e) 23 years

Ans:  (b) 15 years

Explanation:

Present sum of ages of the family = 5 × 20 = 100

Sum of their age excluding the youngest member = 100 – 8 = 92

Sum of 4 members of the family at the birth time of the youngest member = 92 – 4 × 8

                                            = 92 – 32 = 60

Therefore, the required average = 60/4 = 15 years. Ans.

Q. 33. Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

(a) 16 years   (b) 18 years   (c) 28 years    (d) Can’t be determined   (e) None of these

Ans: (e) None of these

Explanation:

Let the ages of Suchin and Rahul be 7x and 9x respectively

Then 9x – 7x = 4

  2x = 4   and x = 2

Therefore, Sachin’ s age = 7x = 7 × 2 = 14 years. Ans.

Q. 34. The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?

(a) 3 : 4    (b) 3 : 5    (c) 4 : 3    (d)  Data in adequate    (e) None of these

Ans:  (e) None of these

Explanation:

Let the ages, P = 6x years   and Q = 7x years

Then,  7x – 6x =4 years so, x = 4 years

Therefore, P’s age = 6 × 4 = 24 and that of Q = 7× 4 = 28

After 4 years, their ages will be = 28 and 32 respectively

And the required ratio = 28 :32 = 7 : 8. Ans.

Q. 35.  The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q’s present age and P’s age after 6 years is 2, what is the total of P’s and Q’s present ages?

(a) 48 years   (b) 52 years   (c) 56 years   (d) Cannot be determined   (e) None of these

Ans: (a) 48 years

Explanation:

Let the present age of P = 5x and that of Q = 7x.

Then 7x – (5x + 6) = 2

 7x – 5x – 6 = 2

  2x = 8   and x = 4

Therefore, the present age of P = 5x = 20 and Q = 28

 Required sum = 20 + 28 = 48 years. Ans.

Q. 36. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present?

(a) 12 years   (b) 15 years    (c) 191/2 years   (d) 21 years   (e) None of these

Ans:  (b) 15 years

Explanation:

Let Arun’s present age = 4x    and Deepak’s present age = 3x

Arun’s age after 6 years = 26

 therefore, Arun’s present age = 20years

then, x = 20/4 = 5

So, Deepak’s present age = 3 x = 3 × 5 = 15 years. Ans.

Q. 37. Present ages of X and Y are in the ratio 5 : 6 respectively. Seven years hence this ratio will become 6 : 7 respectively. What is X’s present age in years?

(a) 35   (b) 42   (c) 19 ½ years     (d) 21 years     (e) None of  these

Ans:  (a) 35 years

Explanation:

Let the present ages of X and Y be 5x and 6x respectively

Then, after 6 years,

  5x +6/6x +6 = 6/7

7 (5x + 6) = 6 ( 6x + 6)

35x + 49 = 36x + 42

Therefore, x = 7

Present age of X = 5x = 5 ×7 = 35 years. Ans.

Q. 38. Present ages of Sameer and Anand are in the ratio of 5 : 6 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?

(a) 24    (b) 27      (c) 40   (d) Cannot be determined   (e) None of these

Ans: (a) 24

Explanation:

Let the present ages of Sameer and Anand  be 5x and 4x respectively

Then, after 3 years,

5x + 3/4x +3 =11/9

9(5x + 3) = 11(4x +3)

45x + 27 = 44x + 33

x = 6

Anand’s age = 4x = 4 ×6 =24 years. Ans.

Q. 39. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?

(a) 16 years   (b) 18 years   (c) 20 years    (d) Cannot be determined   (e) None of these

Q. 40. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years ?

(a) 1 : 4   (b) 2 : 3    (c) 3 : 5    (d) 5 : 6   (e) None of these

Q. 41. The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3: 4. What is the present age of Saransh?

(a) 24 years   (b) 32 years    (c) 34 years    (d) 38 years   (e) None of these

Ans: (d) 38 years

Explanation:

10 years ago sum of their ages = 93 – 30 = 63

Then, the sum of ratio = 9

1 unit of ratio = 63/9 = 7

Therefore, 10 years ago, Saransh’s age = 7 × 4 = 28

Therefore, his present age = 28 + 10 = 38 years. Ans.

Q. 42. The ratio of present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1: 3. What will be the ratio of their ages after 5 years?

(a) 1 : 4   (b) 2 : 3    (c) 3 : 5     (d) 5 : 6   (e) None of these

Ans: (c) 3 : 5

Explanation:

Let their present ages be x and 2x years

5 years back,   x -5/2x-5 = 1/3

3(x-5) = 2x-5

3x -15 = 2x -5

Then , x = 10

Then, present  ages are 10 and 20 years respectively.

Required ratio = 15 : 25 = 3 : 5. Ans.

Q. 43. Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5?

(a) 5 years  (b) 10 years   (c) 20 years    (d) 37 years   (e) None of these

Ans: ( b) 10 years

Explanation:

By close observing the options one by one,  we get the answer (b) 10 years.

 i.e. 10 years ago, their age were, 30 and 50 respectively, ratio = 3 : 5. Ans.

Q. 44. The ratio of the father’s age to his son’s age is 7 : 3. The product of their ages is 756. The ratio of their ages after 6 years will be?

(a) 5 : 2    (b) 2 : 1    (c) 11 : 7    (d) 13 : 9    (e) None of these

Ans: (b) 2 : 1

Explanation:

Let their  ages be 7x and 3x respectively,

Then, 7x × 3x = 756

        21 x² = 756;   x² = 756/21 =36;   x = 6

Their, present ages = 42 and 18 years.

Ages after 6 years = 48 and 24

The required ratio = 48 : 24 = 2 : 1. Ans.

Q. 45. The present ages of three persons are in the proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages ( in years).

(a) 8, 20, 28   (b) 16, 28, 36   (c) 20, 35, 45    (d) 10, 22 ,38   (e) None of these

Ans: (b) 16, 28, 36

Explanation:

Let the present ages be 4x, 7x , 9x

Then, sum of their present ages, 4x + 7x + 9x = 56 + 3 × 8 = 56 + 24

                                                  20x = 80 and x = 4

Therefore, their present ages are 16, 28 , 36 respectively, Ans.

Q. 46. The ratio of the ages of a man and his wife is 4 : 3. After 4 years, this ratio will be 9: 7. If at the time of marriage, the ratio was 5 : 3, then how many years ago were they married?

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

Ans: (c) 12 years

Explanation:

Let their present ages be 4x and 3x

Then, after 4 years, 4x + 4/3x + 4 =9/7

  7( 4x + 4) = 9 (3x +4)

28x + 28 = 27x + 36

x = 8

therefore, their present ages are 32 and 24 years respectively

then, closely observing the options, we get answer (c) 12 years.

i.e. before 12 years their ages are 20 and 12 in the ratio of 5 : 3. Ans.

Q. 47. The ratio between the school ages of Neelam and Shaan is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shaan’s age is 5 : 9, then what is the school age of Shaan?

(a) 25 years   (b) 30 years   (c) 36 years   (d) Cannot be determined    (e) None of these

Ans: (d) Cannot be determined

Explanation:

When taking present ages as 5x and 6x

In further calculation x become cancelled, therefore, it cannot be determined.

Q. 48. The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1 : 1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?

(a) 1 : 3   (b) 2 : 1   (c) 3 : 1   (d) 4 : 1    (e) None of these

Ans: (c) 3 : 1

Explanation:

Let their present ages  be 5x and 3x respectively

Then, 5x -4/3x + 4 = 1/1

 5x -4 = 3x + 4

2x = 8  and x = 4

Their present ages are 20 and 12 respectively

The required ratio = 20 +4 : 12 – 4  = 24 : 8 = 3 : 1. Ans.

Q. 49. Ten years ago, A was half of B’s in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages?

(a)20 years  (b) 30 years   (c) 45 years   (d) 35 years   (e) None of these

Ans: (d) 35 years

Explanation:

Let the present ages be  3x and 4 x years

Then, 10 years ago,

(4x-10)/2 = 3x – 10

4x – 2 = 2 (3x – 10); 2x = 10 and x = 5

So, their present ages are  15 and 20 years respectively

Therefore, the require sum = 15 + 20 = 35. Ans.

Q. 50. A is two years older than B who is twice as old as C. if the total of the ages of A, B and C be 27, then how old is B?

(a) 7   (b) 8   (c) 9   (d) 10     (e) 11

Ans:  (d) 10

Explanation:

Let ‘x’ be the present age of B

A = x + 2. C = x/2

x + 2 + x + x/2 = 27

2x + 2 + x/2 = 27

(2 (2x + 2) +x)/2 = 27

4x + 4 + x = 54

5x = 50  and x = 10 years. Ans.