## Problem Based on ages

#### Problem Based on ages

1. Nikhil is 8 years younger than his brother Rohan. How old will Rohan be when he is twice as old as Nikhil?

1. Suppose, the age of Nikhil is 1 year.
Nikhil is 8 years younger than his brother Rohan.
Therefore, age of Rohan = 1 + 8 = 9 years
After 7 years ,
Nikhil will be 8 years old and Rohan will be 16 years old.

##### Correct Option: D

Suppose, the age of Nikhil is 1 year.
Nikhil is 8 years younger than his brother Rohan.
Therefore, age of Rohan = 1 + 8 = 9 years
After 7 years ,
Nikhil will be 8 years old and Rohan will be 16 years old.

1. The sum of present age of father and his son is 60 years. 6 years ago, father’s age was 5 times the age of the son. After 6 years, son’s age will be :

1. Suppose, the present age of son be P years.
And, the present age of father = Q years
According to question,
The sum of present age of father and his son = 60 years
P + Q = 60 ...(i)
⇒ P = 60 – Q
6 years ago 5 (P – 6) = Q – 6
⇒ 5P – 30 = Q – 6
⇒ 5P – Q = 30 – 6 = 24 ...(ii)
After putting the value of P in equation (ii), we get:
5 (60 – Q) – Q = 24
⇒ 300 – 5Q – Q = 24
⇒ 300 – 6Q = 24
⇒ 6Q = 300 – 24

 ∴ Q = 276 = 48 years 6

##### Correct Option: C

Suppose, the present age of son be P years.
And, the present age of father = Q years
According to question,
The sum of present age of father and his son = 60 years
P + Q = 60 ...(i)
⇒ P = 60 – Q
6 years ago 5 (P – 6) = Q – 6
⇒ 5P – 30 = Q – 6
⇒ 5P – Q = 30 – 6 = 24 ...(ii)
After putting the value of P in equation (ii), we get:
5 (60 – Q) – Q = 24
⇒ 300 – 5Q – Q = 24
⇒ 300 – 6Q = 24
⇒ 6Q = 300 – 24

 ∴ Q = 276 = 48 years 6

∴ P = 60 – 46 = 14 years
After 6 years, the age of P = (14 + 6) years = 20 years

1. The present age of Sanyal is 3 times the present age of his son. Six years hence, the ratio of their ages will be 5 : 2 respectively. The present age of Sanyal is:

1. Let us assume the present age of son be x then his father present age will be 3x.

##### Correct Option: C

Let us assume the present age of son be x then his father present age will be 3x.
According to question,
Six years hence, the ratio of their ages will be 5 : 2 respectively
(3x + 6)/(x+6) = 5/2
⇒ (3x + 6)2 = 5(x+6)
⇒ 6x + 12 = 5x + 30
∴ x = 18
Hence, age of Sanyal = 3 x 18 = 54 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