## Problem Based on ages

#### Problem Based on ages

1. The sum of the ages of a father and a son presently is 70 years. After 10 years the son’s age is exactly half that of the father’s. What are their ages now?

1. Suppose the present age of son = P years
The present age of father = Q years
P + Q = 70 ...(i)
According to question, 2(P + 10) = Q + 10
⇒ 2P + 20 = Q + 10
⇒ 2P – Q = –10 ....(ii)

##### Correct Option: B

Suppose the present age of son = P years
The present age of father = Q years
P + Q = 70 ...(i)
According to question, 2(P + 10) = Q + 10
⇒ 2P + 20 = Q + 10
⇒ 2P – Q = –10 ....(ii)
From equations (i) and (ii) , we get
3P = 70 – 10 = 60 ⇒ P = 20 years
∴ Q = 70 – 20 = 50 years

1. The average weight of 8 persons of a family is increased by 1 kg when one of the members whose weight is 60 kg is replaced by a new person. The weight of the new person (in kg) is

1. Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
Using formula ,
∴ Weight of new person = Weight of replaced person + n × increase in Average

##### Correct Option: B

Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
Using formula ,
∴ Weight of new person = Weight of replaced person + n × increase in Average
Weight of new person = 60 + 8 × 1 = 68 kg

1. The average age of three friends A, B, C is 20 years. The average age of A and B is 19 years. What is the age of C?

1. Given that :- The average age of three friends A, B, C = 20 years.
Total age of three friends A, B, C = 3 x 20 = 60 years.
The average age of A and B = 19 years.
Total age of of A and B = 2 x 19 = 38 years.
∴ Age of C = Total age of three friends A , B and C - Total age of of A and B

##### Correct Option: C

Given that :- The average age of three friends A, B, C = 20 years.
Total age of three friends A, B, C = 3 x 20 = 60 years.
The average age of A and B = 19 years.
Total age of of A and B = 2 x 19 = 38 years.
∴ Age of C = Total age of three friends A , B and C - Total age of of A and B
Age of C = 60 – 38 = 22 years

1. The sum of the ages of a daughter and mother is 56 years. After 4 years, the age of the mother will be 3 times that of the daughter. Their respective ages are.

1. Suppose the age of mother be P years and that of daughter’s age be Q years.
According to question P + Q = 56 .........(i)
After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)

##### Correct Option: B

Suppose the age of mother be P years and that of daughter’s age be Q years.
According to question P + Q = 56 .........(i)
After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)
On solving equations (i) and (ii) , we get
Q = 12 years
∴ P = 56 – 12 = 44 years
Hence , the age of mother is 44 years and her daughter’s age is 12 years .

1. A father tells his son, “I was 3 times of your present age when you were born.” If the father’s present age is 48 years, how old was the boy 4 years ago?

1. Suppose that son’s age before 4 years = P
Present age of the son = P + 4
At son’s birth father’s age = 3(P + 4) = 3P + 12
The father’s present age = (3P +12) + (P + 4) = 48
⇒ 4P = 48 years – 16 = 32

##### Correct Option: B

Suppose that son’s age before 4 years = P
Present age of the son = P + 4
At son’s birth father’s age = 3(P + 4) = 3P + 12
The father’s present age = (3P +12) + (P + 4) = 48
⇒ 4P = 48 years – 16 = 32
⇒ P = 8 years
Therefore, 4 years ago the boy was = 12 – 4 = 8 years