## Problem Based on ages

#### Problem Based on ages

1. The ages of Samir and Saurabh are in the ratio of 8 : 15 respectively . After 9 years the ratio of their ages will be 11 : 18. What is the difference between their ages in years?

1. Let the present ages of Samir and Saurabh are 8a and 15a years respectively.

##### Correct Option: B

Let the present ages of Samir and Saurabh are 8a and 15a years respectively ; .
After 9 years the ages of Samir and Saurabh will be 8a + 9 and 15a + 9.
According to question,
After 9 years the ratio of their ages will be 11 : 18, then
(8a + 9)/ = 11/18
⇒ (8x + 9) x 18 = 11 x (15a + 9)
⇒ 144a + 162 = 165a + 99
⇒ 21a = 63
∴ a = 3
Hence, difference of their ages = 15a - 8a = 7a = 7 x 3 = 21 years

1. The ratio of the present ages of Suresh and his daughter is 2 : 1. Six years hence, the ratio of their ages would be 23 : 13. Find the present age of Suresh?

1. Let us assume the present ages of Suresh and his daughter be 2x and x years respectively.

##### Correct Option: B

Let the present ages of Suresh and his daughter be 2x and x years respectively; then
According to question,
Six years hence, the ratio of their ages would be 23 : 13
(2x + 6) / (x + 6) = 23/13
⇒ (2x + 6) 13 = 23 (x + 6)
⇒ 26x + 78 = 23x + 138
⇒ 3x = 60
∴ x = 20
Hence, present age of Suresh = 2 x 10 = 40 years

1. The present age of father is 34 years more than that of his son. 12 years ago, father's age was 18 times the age of his son. The present age of son in years is :

1. Let us assume the present ages of son be Y then his father present age will be Y + 34 years.

##### Correct Option: B

Let us assume the present ages of son be Y then his father present age will be Y + 34 years. then
12 years ago, father's age = Y + 34 -12
12 years ago, Son's age = Y - 12
Now according to question,
12 years ago, father's age was 18 times the age of his son. then
18( Y - 12 ) = Y + 34 - 12
⇒ 18Y - 216 = Y + 22
⇒ 17Y = 238
∴ Y = 14
Hence, present age of his son = 14 years.

1. The ratio of the ages of two persons is 4 : 7 and age of then is more than other by 30 years. The sum of their ages in years is:

1. Let the present ages of two person be 4x and 7x years respectively;

##### Correct Option: B

Let the present ages of two person be 4x and 7x years respectively; then according to question,
7x = 30 + 4x
⇒ 3x = 30
∴ x = 10
Hence, sum of their ages = 4x + 7x = 11x = 11 x 10 = 110 years

1. A father is older than his first son by 30 years, the first son is older than the second son by 10 years. If the sum of their ages be 95 years, find the age of father.

1. Let us assume the age of second son be Y, then age of first son will be Y + 10 and age of father will be (Y + 10 + 30) years respectively;

##### Correct Option: C

Let us assume the age of second son be Y, then age of first son will be Y + 10 and age of father will be (Y + 10 + 30) years respectively;
then according to question,
sum of their ages be 95 years.
x + x + 10 + x + 10 + 30 = 95
⇒ 3x = 95 - 50
⇒ 3x = 45
∴ x = 15
age of the father = x + 10 + 30
Hence, age of the father = 15 + 10 + 30 = 55 years.