## Problem Based on ages

#### Problem Based on ages

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. A is 16 years older than B. But half the age of B is equal to 1/3 of A’s age. Find their present age.

1. Suppose the age of A is P years and that of B is Q years.
According to question,
age of A = age of B + 16 years
P = Q + 16
⇒ P – Q = 16 ......(i)

 Again, age of A = age of B 3 2

 ⇒ P = Q 3 2

##### Correct Option: B

Suppose the age of A is P years and that of B is Q years.
According to question,
age of A = age of B + 16 years
P = Q + 16
⇒ P – Q = 16 ......(i)

 Again, age of A = age of B 3 2

 ⇒ P = Q 3 2

⇒ 2P = 3Q
⇒ 2P – 3Q = 0 ......(ii)
From equations (i) and (ii) , we get
P = 48 years
∴ Q = 48 – 16 = 32 years
Thus, age of A = 48 years and age of B = 32 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. 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