## 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. 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 }

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. A father is 5 times as old as his son. His son is 6 years old. After how many years, will the father be 4 times as old as his son?

1. Age of son = 6 years
Age of father = 6 × 5 = 30 years
Let after P years father will be 4 times of son.
According to question ,
⇒ 30 + P = 4 (6 + P)
⇒ 4P – P = 30 – 24

##### Correct Option: D

Age of son = 6 years
Age of father = 6 × 5 = 30 years
Let after P years father will be 4 times of son.
According to question ,
⇒ 30 + P = 4 (6 + P)
⇒ 4P – P = 30 – 24
⇒ 3P = 6
⇒ P = 2 years
Hence, after 2 years father will be 4 times of son.

1. Mahesh is ‘60’ years old. Ram is ‘5’ years junior to Mahesh and '4’ years senior to Raju. The youngest brother of Raju is Babu and he is ‘6’ years junior to him. What is the age difference between Mahesh and Babu?

1. Age of Mahesh = 60 years
Age of Ram = Age of Mahesh - 5 years = 60 – 5 = 55 years
Age of Raju = Age of Ram - 4 years = 55 – 4 = 51 years
Age of Babu = Age of Raju - 6 years = 51 – 6 = 45 years

##### Correct Option: B

Age of Mahesh = 60 years
Age of Ram = Age of Mahesh - 5 years = 60 – 5 = 55 years
Age of Raju = Age of Ram - 4 years = 55 – 4 = 51 years
Age of Babu = Age of Raju - 6 years = 51 – 6 = 45 years
Age difference between Mahesh and Babu = 60 – 45 = 15 years