## Problem Based on ages

#### Problem Based on ages

1. A mother is 5 times older than her daughter. After 5 years, she would be 3 times older than her daughter. Find the mother’s present age.

1. Suppose the present age of daughter = P years
Therefore, the present age of mother = 5P years
According to question,
After 5 years, ( the present age of mother + 5 years ) = 3 × ( the present age of daughter + 5 years )
5P + 5 = 3 (P + 5)
⇒ 5P + 5 = 3P + 15
⇒ 5P – 3P = 15 – 5
⇒ 2P = 10

##### Correct Option: C

Suppose the present age of daughter = P years
Therefore, the present age of mother = 5P years
According to question,
After 5 years, ( the present age of mother + 5 years ) = 3 × ( the present age of daughter + 5 years )
5P + 5 = 3 (P + 5)
⇒ 5P + 5 = 3P + 15
⇒ 5P – 3P = 15 – 5
⇒ 2P = 10

 ∴ P = 10 = 5 2

Therefore , Present age of mother = 5P = 5 × 5 = 25 years

1. The sum of ages of 4 children born at intervals of 4 years each is 60. What is the age of the youngest child?

1. Suppose the age of the youngest child = P years
Therefore, the ages of the other children = P + 4, P + 8 and P + 12 years
According to question ,
The sum of ages of 4 children born at intervals of 4 years each = 60.
P + P + 4 + P + 8 + P + 12 = 60
⇒ 4P + 24 = 60
⇒ 4P = 60 – 24

##### Correct Option: B

Suppose the age of the youngest child = P years
Therefore, the ages of the other children = P + 4, P + 8 and P + 12 years
According to question ,
The sum of ages of 4 children born at intervals of 4 years each = 60.
P + P + 4 + P + 8 + P + 12 = 60
⇒ 4P + 24 = 60
⇒ 4P = 60 – 24 = 36

 ⇒ P = 36 = 9 years 4

Therefore , the age of the youngest child is 9 years .

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