__Problems on Ages Practice Quiz – Set 2__**1.**

**Ram is two years older than Shyam who is twice as old as Mohan. If the total of the ages of Ram, Shyam and Mohan be 27, the how old is Shyam ?**

a) 7 years

b) 8 years

c) 9 years

d) 10 years

**2.**

**The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be ?**

a) 12 years

b) 14 years

c) 16 years

d) 18 years

e) 20 years

**3.**

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

a) 16 years

b) 18 years

c) 24.5 years

d) 26 years

e) 28 years

**4.**

**The age of father 10 years ago was thrice the age of his son. 10 years hence, father's age will be twice that of his son. The ratio of their present ages is :**

a) 5 : 2

b) 9 : 2

c) 7 : 3

d) 13 : 4

e) 15 : 7

**5.**

**Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents ?**

a) 2 years

b) 4 years

c) 6 years

d) 8 years

e) 10 years

**6.**

**One year ago, a man was 7 times as old as his son. Now his age is equal to the square of his son's age. The present age of the man will be :**

a) 7 years

b) 36 years

c) 49 years

d) 64 years

e) None of these

**7.**

**The ratio between the present ages of Ravi and Jai is 3:2. If Ravi was 6 years older to Jai four years back, how old is Jai now ?**

a) 6 years

b) 12 years

c) 18 years

d) Data inadequate

e) None of these

**8.**

**A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was :**

a) 14 years

b) 19 years

c) 33 years

d) 38 years

e) 41 years

**9.**

**The ages of two persons are in the ratio of 5 : 7. Sixteen years ago, their ages were in the ratio of 3 : 5. Their present ages are :**

a) 30 years, 44 years

b) 40 years, 56 years

c) 35 years, 52 years

d) 45 years, 60 years

e) None of these

**10.**

**The present ages of three persons in 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) 20, 35, 45

c) 16, 28, 36

d) 20, 28, 36

e) None of these

**Solutions:**

**1. D)**Let Mohan's age be x years. Then,

Shyam's age = 2x years.

Ram's age = (2x + 2) years.

∴ (2x + 2) + 2x + x = 27

⇒ 5x = 25 ⇒ x = 5

Hence, Shyam's age = 2x = 10 years.

**2. D)**Let the present ages of son and father be x and (60 − x) years respectively.

Then, (60 − x) − 6 = 5(x − 6)

⇒ 54 − x = 5x − 30

⇒ 6x = 84

⇒ x = 14.

∴ Son's age after 6 years = (x + 6) = 20 years.

**3. C)**Let Rahul's age be x years.

Then, Sachin's age = (x − 7) years.

Therefore, (x – 7)/x = 7/9

⇒ 9x − 63 = 7x

⇒ 2x = 63

⇒ x = 31.5

Hence, Sachin's age = (x − 7) = 24.5 years.

**4. B)**Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

⇒ 3x + 20 = 2x + 40

⇒ x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7
: 3.

**5. C)**Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 +
4) years = 42 years.

Required difference = (42 − 36) years = 6 years.

**6. C)**Let the present age of the son be x years.

Man's present age = [7(x − 1) + 1]years = (7x −
6)years

∴ 7x − 6 = x^2 ⇒ x^2 − 7x + 6 = 0

⇒ (x − 6)(x − 1) = 0 ⇒ x = 6 or x = 1

∴ Man's present age = (7 x 6 − 6)years =
36 years.

**7. C)**Let Ravi's age = 3x years. Then, Jai's age = 2x years

(3x − 4) = 2x − 4 + 6 ⇒ x = 6

Jai's present age = (2 x 6) years = 12 years.

**8. A)**Let the son's present age be x years. Then, (38 − x) = x

⇒ 2x = 38

⇒ x = 19

∴ Son's age 5 years back (19 - 5) = 14 years.

**9. C)**Let their present ages be 5x years and 7x years. Then,

(5x – 16)/(7x – 16) = 3/5 ⇒ 5(5x − 16) = 3(7x − 16)

⇒ 4x = (80 − 48) = 32 ⇒ x = 8

Hence, their present ages are 40 years and 56 years

**10. B)**Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

⇒ 20x = 80

⇒ x = 4.

Their present ages are 4x = 16 years, 7x = 28 years
and 9x = 36 years respectively.