Problem Based on ages
 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?

View Hint View Answer Discuss in Forum
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
 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

View Hint View Answer Discuss in Forum
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 AverageCorrect 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
 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?

View Hint View Answer Discuss in Forum
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 BCorrect 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
 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.

View Hint View Answer Discuss in Forum
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 .
 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?

View Hint View Answer Discuss in Forum
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 = 32Correct 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