## Problem Based on ages

#### Problem Based on ages

1. 20 years ago, Antony’s age was 1/2 of what his age now is. What is his age now?

1. Suppose the present age of Antony is P years.

 20 years ago his age was P years 2

##### Correct Option: B

Suppose the present age of Antony is P years.

 20 years ago his age was P years 2
According to question ,
 the present age of Antony - 20 years = the present age of Antony 2

 ⇒ P - 20 = P 2

⇒ 2P – 40 = P
⇒ 2P – P = 40
∴ P = 40 years
Hence , the present age of Antony is 40 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. A man was 32 years of age when he had his first son. His wife was 35 years of age when his son attained the age of 7 years. The difference between the age of the father and the mother is ______.

1. The age of father when his son attained the age of 7 years = 32 + 7 = 39 years
The age of mother when her son attained the age of 7 years = 35 years
∴ Required difference = The age of father when his son attained the age of 7 years - The age of mother when her son attained the age of 7 years

##### Correct Option: D

The age of father when his son attained the age of 7 years = 32 + 7 = 39 years
∴ Required difference = The age of father when his son attained the age of 7 years - The age of mother when her son attained the age of 7 years
The difference between the ages of father and mother = (39 – 35) years = 4 years

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 average age of the present ages of Amit and Anil is 32 years. If Amit is 6 years older than Anil, what is Anil’s present age?

1. The average age of the present ages of Amit and Anil = 32 years
Total age of Amit and Anil = 2 × 32 = 64 years
Suppose, age of Anil = P years
∴ Age of Amit = P + 6 years
According to the question, P + P + 6 = 64
⇒ 2P = 64 – 6 = 58

##### Correct Option: D

The average age of the present ages of Amit and Anil = 32 years
Total age of Amit and Anil = 2 × 32 = 64 years
Suppose, age of Anil = P years
∴ Age of Amit = P + 6 years
According to the question, P + P + 6 = 64
⇒ 2P = 64 – 6 = 58

 ∴ P = 58 = 29 years 2

Hence , Anil’s present age is 29 years .