## Problem Based on ages

#### Problem Based on ages

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 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. 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. 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. 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