## Problem Based on ages

#### Problem Based on ages

1. Your mother is 4 years younger than your father who is 6 times older than you. If your age is 6 years, what is your mother’s age?

1. Given :- The age of person is 6 years
His father’s age = 6 × 6 = 36 years

##### Correct Option: D

Given :- The age of person is 6 years
His father’s age = 6 × 6 = 36 years
Therefore, the age of his mother = His father’s age - 4 years = 36 – 4 = 32 years

1. The total age of a mother and her daughter is 60 years. The difference between their ages is 30 years. Find out the age of the mother.

1. Suppose, daughter’s age is P years.
Therefore, mother’s age will be ( P + 30 ) years.
The total age of a mother and her daughter = 60 years.
⇒ P + ( P + 30 ) = 60
⇒ 2P = 60 – 30

##### Correct Option: B

Suppose, daughter’s age is P years.
Therefore, mother’s age will be ( P + 30 ) years.
The total age of a mother and her daughter = 60 years.
⇒ P + ( P + 30 ) = 60
⇒ 2P = 60 – 30

 ∴ P = 30 = 15 2

Therefore , the age of the mother is 15 years .

1. ‘X’ and her grandfather differ in their ages by 50 years. After 6 years, if the sum of their ages is 152, their present ages are

1. Suppose the present age of X = P years
Her grandfather’s present age = P + 50 years
According to question P + 6 + P + 50 + 6
⇒ 2P + 62 = 152
⇒ 2P = 152 – 60

##### Correct Option: C

Suppose the present age of X = P years
Her grandfather’s present age = P + 50 years
According to question P + 6 + P + 50 + 6
⇒ 2P + 62 = 152
⇒ 2P = 152 – 60

 ∴ present age of 'X' = P = 90 = 45 Years 2

and present age of grand father = P + 50 = 45 +50 = 95 years

1. Today is Ketan’s birthday. One year from today he will be twice as old as he was 10 years ago. How old is Ketan today?

1. Suppose the present age of Ketan is P years.
According to question,
present age of Ketan + 1 year = 2 ( present age of Ketan - 10 years )
P + 1 = 2 (P – 10)
⇒ P + 1 = 2P – 20
⇒ 2P – P = 20 + 1

##### Correct Option: C

Suppose the present age of Ketan is P years.
According to question,
present age of Ketan + 1 year = 2 ( present age of Ketan - 10 years )
P + 1 = 2 (P – 10)
⇒ P + 1 = 2P – 20
⇒ 2P – P = 20 + 1
∴ P = 21 years
Therefore ,present age of Ketan is 21 years .

1. A father’s age is now three times that of his elder daughter. 5 years back, his age was 8 times that of his younger daughter. If the difference of ages of the two daughters is 5 years, what is the age of the father now?

1. Suppose the present age of younger daughter is P years.
Given : - Present age of the elder daughter - the present age of younger daughter = 5
∴ Present age of the elder daughter = P + 5 years
Present age of the father = 3 × Present age of the elder daughter
Present age of the father = 3(P + 5) years.
According to the question,
5 years before, 8 × ( the present age of younger daughter - 5 years ) = Present age of the father - 5 years
⇒ 8 (P – 5) = (3P + 15) – 5

##### Correct Option: D

Suppose the present age of younger daughter is P years.
Given : - Present age of the elder daughter - the present age of younger daughter = 5
∴ Present age of the elder daughter = P + 5 years
Present age of the father = 3 × Present age of the elder daughter
Present age of the father = 3(P + 5) years.
According to the question,
5 years before, 8 × ( the present age of younger daughter - 5 years ) = Present age of the father - 5 years
⇒ 8 (P – 5) = (3P + 15) – 5
⇒ 8P – 40 = 3P + 10
⇒ 8P – 3P = 10 + 40

 ∴ P = 50 = 10 years 5

Present age of father = 3(P + 5) = 3 × 10 + 15 = 45 years { ∴ putting , P = 10 }