## Problem Based on ages

#### Problem Based on ages

1. A was born 5 years before B, B is 4 years older than C and 3 years younger to D. If A is now 17 years old, how old is D?

1. Here , Present age of A = 17 years
Age of B = age of A - 5 years = 17 – 5 = 12 years
Age of C = age of B – 4 years =12 – 4 = 8 years

##### Correct Option: B

Here , Present age of A = 17 years
Age of B = age of A - 5 years = 17 – 5 = 12 years
Age of C = age of B – 4 years =12 – 4 = 8 years
Age of D = Age of B + 3 years =12 + 3 = 15 years

1. Ashok’s mother was 3 times as old as Ashok 5 years ago. After 5 years she will be twice as old as Ashok. How old is Ashok today?

1. Suppose the present age of Ashok is P years and that of his mother is Q years.
5 years ago 3 ( P – 5 ) = ( Q – 5 )
⇒ 3P – 15 = Q – 5

##### Correct Option: B

Suppose the present age of Ashok is P years and that of his mother is Q years.
5 years ago ,
3 × ( age of Ashok - 5 ) = ( age of Ashok 's mother - 5 )
3 ( P – 5 ) = ( Q – 5 )
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 ....(i)
5 years after,
2 × ( age of Ashok + 5 ) = ( age of Ashok 's mother + 5 )
2 ( P + 5 ) = ( Q + 5 )
⇒ 2P + 10 = Q + 5
⇒ 2P – Q = – 5 ....(ii)
From equations (i) and (ii) , we get
P = 15 years
Hence , the present age of Ashok is 15 years .

1. Hari is twice as old as Johnny, who is three years older than Rahul. If Hari’s age is five times Rahul’s age, how old is Johnny?

1. Suppose the age of Johnny is P years and that of Rahul is Q years.
According to question ,
Age of Hari = 2 × Age of Johnny = 2P
And age of Hari = 5 × Age of Rahul = 5Q
⇒ 2P = 5Q
⇒ 2P – 5Q = 0 ........(i)
Again age of Johnny = Age of Rahul + 3 years
⇒ P = 3 + Q
⇒ P – Q = 3........ (ii)

##### Correct Option: C

Suppose the age of Johnny is P years and that of Rahul is Q years.
According to question ,
Age of Hari = 2 × Age of Johnny = 2P
And age of Hari = 5 × Age of Rahul = 5Q
⇒ 2P = 5Q
⇒ 2P – 5Q = 0 ........(i)
Again age of Johnny = Age of Rahul + 3 years
⇒ P = 3 + Q
⇒ P – Q = 3........ (ii)
On solving equations (i) and (ii), we get
Q = 2
∴ Age of Johnny = 3 + Q = 3 + 2 = 5 years
Hence , the age of Johnny is 5 years .

1. In a family, mother’s age is twice that of daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father?

1. Suppose the age of daughter is P years.
Age of brother = age of daughter + 5 years = P + 5 years
Age of mother = 2 × age of daughter = 2P years
According to question ,
∴ Age of mother - 20 years = Age of brother
⇒ 2P – 20 = P + 5
⇒ 2P – P = 5 + 20

##### Correct Option: B

Suppose the age of daughter is P years.
Age of brother = age of daughter + 5 years = P + 5 years
Age of mother = 2 × age of daughter = 2P years
According to question ,
∴ Age of mother - 20 years = Age of brother
⇒ 2P – 20 = P + 5
⇒ 2P – P = 5 + 20
⇒ P = 25 years
Age of mother = 2P = 2 × 25 = 50 years
Age of father = Age of mother + 10 years = 50 + 10 = 60 years