problems on ages

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6. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A. 14 years B. 18 years
C. 20 years D. 22 years

Answer: Option D

Explanation:

 

Let the son’s present age be x years. Then, man’s present age = (x + 24) years.

(x + 24) + 2 = 2(x + 2)

x + 26 = 2x + 4

x = 22.
7. 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

Answer: Option A

Explanation:

 

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

 

Then, (6x + 6) + 4 = 11
(5x + 6) + 4 10

10(6x + 10) = 11(5x + 10)

5x = 10

x = 2.

Sagar’s present age = (5x + 6) = 16 years.
8. 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. 18 years D. 20 years

Answer: Option D

Explanation:

 

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..
9. 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. 19 and half D. 21 years

Answer: Option B

Explanation:

 

Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,

4x + 6 = 26       4x = 20

x = 5.

Deepak’s age = 3x = 15 years.
10. Sachin is younger than Rahul by 7 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. 24.5 years
E. None of these

Answer: Option D

Explanation:

 

Let Rahul’s age be x years.

Then, Sachin’s age = (x – 7) years.

 

x – 7 = 7
x 9

9x – 63 = 7x

2x = 63

x = 31.5

Hence, Sachin’s age =(x – 7) = 24.5 years.
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