## Problem Based on ages

#### Problem Based on ages

1. Neela is now 3 times as old as her daughter Leela. Ten years back, Neela was 5 times as old as Leela. The age of Leela is

1. Suppose the present age of Leela is P years.
Therefore, the present age of Neela = 3P years
10 years ago ,5 × ( the present age of Leela - 10 years ) = ( the present age of Neela - 10 years )
5 (P – 10) = (3P – 10)

##### Correct Option: D

Suppose the present age of Leela is P years.
Therefore, the present age of Neela = 3P years
10 years ago ,5 × ( the present age of Leela - 10 years ) = ( the present age of Neela - 10 years )
5 (P – 10) = (3P – 10)
⇒ 5P – 50 = 3P – 10
⇒ 5P – 3P = 50 – 10
⇒ 2P = 40

 ∴ P = 40 = 20 years 2

Therefore , the present age of Leela is 20 years.

1. 2 years ago a mother was 4 times as old as her son. 6 years from now her age will become more than double her son’s age by 10 years. What is the present ratio of their ages?

1. Suppose the present age of son = P years
Present age of mother = Q years
According to question,
4 (P – 2) = Q – 2
⇒ 4P – 8 = Q – 2
⇒ 4P – Q = 6 ...(i)
2 (P + 6) + 10 = Q + 6
⇒ 2P + 12 + 10 = Q + 6

##### Correct Option: B

Suppose the present age of son = P years
Present age of mother = Q years
According to question,
4 (P – 2) = Q – 2
⇒ 4P – 8 = Q – 2
⇒ 4P – Q = 6 ...(i)
2 (P + 6) + 10 = Q + 6
⇒ 2P + 12 + 10 = Q + 6
⇒ 2P – Q = –16 ...(ii)
From equations (i) and (ii)
P = 11
∴ Q = 4 × 11 – 6 = 38
Required the present ratio of their ages = 38 : 11

1. Mother was three times the age of her daughter 5 years ago. After 5 years, mother will be twice as old as her daughter. How old is the daughter today?

1. Suppose the present age of daughter = P years
and, the present age of mother = Q years
According to questions,
5 years ago , 3 × ( the present age of daughter - 5 ) = ( the present age of mother - 5 )
3 (P – 5) = (Q – 5)
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 .......(i)
After five years , 2 × ( the present age of daughter + 5 ) = ( the present age of mother + 5 )
2 (P + 5) = Q + 5
⇒ 2P + 10 = Q + 5

##### Correct Option: C

Suppose the present age of daughter = P years
and, the present age of mother = Q years
According to questions,
5 years ago , 3 × ( the present age of daughter - 5 ) = ( the present age of mother - 5 )
3 (P – 5) = (Q – 5)
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 .......(i)
After five years , 2 × ( the present age of daughter + 5 ) = ( the present age of mother + 5 )
2 (P + 5) = Q + 5
⇒ 2P + 10 = Q + 5
⇒ 2P – Q = –5 .......(ii)
From equations (i) and (ii) , we get
3P – 2P = 10 – (–5)
⇒ P = 15 years
Hence, the present age of daughter is 15 years .

1. The age of a father is twice that of his son’s at present age. After 5 years the sum of their ages will be 85. How old are they now?

1. Suppose the present age of son = P years
Age of father = 2P years
According to question
P + 5 + 2P + 5 = 85
⇒ 3P + 10 = 85
⇒ 3P = 85 – 10 = 75

##### Correct Option: D

Suppose the present age of son = P years
Age of father = 2P years
According to question
P + 5 + 2P + 5 = 85
⇒ 3P + 10 = 85
⇒ 3P = 85 – 10 = 75

 Present age of son P = 75 = 25 Years 2

and Father's present age = 2P = 50 years

1. Amit was born 5 years before Rakesh, Rakesh is 3 years younger to Anil. If Amit is now 17 years old, how old is Anil?

1. The present age of Amit = 17 years
5 years before , age of Rakesh = The present age of Amit - 5 years = 17 – 5 = 12 years

##### Correct Option: C

The present age of Amit = 17 years
5 years before , age of Rakesh = The present age of Amit - 5 years = 17 – 5 = 12 years
∴ Age of Anil = age of Rakesh + 3 years = 12 + 3 = 15 years