## Problem Based on ages

#### Problem Based on ages

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. A is older by 4 years to B at one stage. After 16 years of this stage, A will be thrice his present age and B will be five times his present age. How old would A and B be two years before the initially indicated stage?

1. Suppose the ages of A and B are P and Q years respectively.
According to question
Age of A = Age of B + 4 years
⇒ P = Q + 4
After 16 years , Age of A + 16 = 3 x Age of A
⇒ P + 16 = 3P
and Age of B + 16 = 5 x Age of B
⇒ Q + 16 = 5Q
⇒ P = 8 and Q = 4

##### Correct Option: C

Suppose the ages of A and B are P and Q years respectively.
According to question
Age of A = Age of B + 4 years
⇒ P = Q + 4
After 16 years , Age of A + 16 = 3 x Age of A
⇒ P + 16 = 3P
and Age of B + 16 = 5 x Age of B
⇒ Q + 16 = 5Q
⇒ P = 8 and Q = 4
2 years ago their ages
Age of A = 8 – 2 = 6 years
Age of B = 4 – 2 = 2 years

1. Father is 5 years older than mother and mother’s age now is thrice the age of the daughter. The daughter is now 10 years old. What was the father’s age when the daughter was born?

1. Here , Father = F , Mother = M and Daughter = D
According to question
Age of F = Age of M + 5,
Age of M = 3 × Age of D and Age of D = 10 years
∴ Age of M = 3 × 10 = 30 years

##### Correct Option: C

Here , Father = F , Mother = M and Daughter = D
According to question
Age of F = Age of M + 5,
Age of M = 3 × Age of D and Age of D = 10 years
∴ Age of M = 3 × 10 = 30 years
Therefore, father’s present age = 30 + 5 = 35 years
Required answer = father’s present age - 10 years = 35 – 10 = 25 years

1. The age of Ram is double that of Shyam and half the of Sohan. Shyam is older than Mohan. Who is the oldest?

1. Suppose the age of Shyam = P years
According to question ,
Age of Ram = 2 × age of Shyam = 2P years
Age of Sohan = 4 × age of Shyam = 4P years

##### Correct Option: C

Suppose the age of Shyam = P years
According to question ,
Age of Ram = 2 × age of Shyam = 2P years
Age of Sohan = 4 × age of Shyam = 4P years
∴ Shyam > Mohan
So, Sohan (4P) > Ram (2P) > Shyam (P) > Mohan
∴ Sohan is the oldest.

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.