## Problem Based on ages

#### Problem Based on ages

1. The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1:3. What are the ages of A and B?

1. Let us assume the the ages of A and B be 3x and 11x years.

##### Correct Option: A

Let us assume the ages of A and B be 3x and 11x years; then
After 3 years the ages of A and B will be 3x + 3 and 11x + 3.
According to question,
After 3 years the ratio of the ages becomes 1: 3,
(3x + 3)/(11x + 3) = 1/3
⇒ 3 (3x + 3) = 1 (11x + 3)
⇒ 9x + 9 = 11x + 3
⇒ 2x = 6
∴ x = 3
Hence, their present age, 3x = 3 x 3 = 9 years; 11x = 11 x 3 =33 years

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

1. Method 1
Let us assume the present age of B and A be x and ( x + 9 ) years.

Method 2
Let us assume the present age of B and A be x and y years.

##### Correct Option: B

Method 1
Let the present age of B and A be x and ( x + 9 ) years; then,
Age of B and A after 10 years will be x + 10 and x + 9 + 10;
According to question,
In 10 years A will be twice as old as B was 10 years ago
2(x - 10) = x + 9 + 10
2x - 20 = x + 19
⇒ 2x - x = 19 + 20
∴ x = 39 years

Method 2
Let us assume the present age of B and A be x and y years.
According to question,
A is now 9 years older than B,
y = x + 9...........(1)
Again according to question,
In 10 years A will be twice as old as B was 10 years ago
y + 10 = 2( x - 10)................. (2)
now put the value of y from equation (1) in above equation (2)
x + 9 +10 = 2x - 20
⇒ 2x - x = 19 + 20
⇒ x = 39 years
So Present age of B = 39 years.

1. Radha get married 6 years ago. Today her age is 11/4 times her age at the time of marriage. Her son's age is 1/10 times her age. Her son's age is :

1. Let us assume the present age of Radha be Y years; then
Before 6 years Radha's age will be Y - 6 years.

##### Correct Option: C

Let us assume the present age of Radha be Y years; then
Before 6 years Radha's age will be Y - 6 years.
According to question,
Today her age is 11/4 times her age at the time of marriage,
5/4 ( Y - 6 ) = Y ( Since 11/4 = 5/4 )
⇒ 5Y - 30 = 4Y
∴ Y = 30 years
Hence, her son's age = 30 x 1/10 =3 years

1. Two years ago, the ratio of Ram's and Mohan's age was 3 : 2 and at present 7 : 5. What are their present ages?

1. The ratio of Ram's and Mohan's present age is 7 : 5.
Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.

##### Correct Option: A

The ratio of Ram's and Mohan's present age is 7 : 5.
Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.
2 Years ago the age of Ram and Mohan will be 7Y - 2 and 5Y - 2 years.
According to question,
Two years ago, the ratio of Ram's and Mohan's age was 3 : 2, then
(7Y -2)/(5Y - 2) = 3/2
⇒ (7Y -2) x 2 = 3 x (5Y - 2)
⇒ 14Y - 4 = 15Y - 6
∴ Y = 2
Hence, their present ages = 7 x 2 = 14 years and 5 x 2 = 10 year

1. One year ago, the ratio of Yamini and Gamini's was 6 : 7 respectively. Four year hence, the ratio would become 7 : 8. Find the age of Gamini ?

1. Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively.

##### Correct Option: C

Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively; then
(6P + 5)/(7P + 5) = 7/8
⇒ (6P + 5) x 8 = 7 x (7P + 5)
⇒ 48P + 40 = 49P + 35
∴ P = 5
Hence, present ago of Gamini = 7P + 1 = 7 x 5 + 1 = 36 years