Question

The ratio of ages of father and son is 7:2. Five years ago the product of their ages was 150. What is the age of the father?

A) 30 years B) 45 years C) 35 years D) 40 years

Answer 1

ANSWER:

• Age of father = 35 years [Correct Option = (A) ]

GIVEN:

• The ratio of ages of father and son is 7:2. Five years ago the product of their ages was 150.

TO FIND:

• Age of father.

SOLUTION:

Let the ratio of father and son be 7x and 2x.

5 years ago Father's age = (7x-5)

5 years ago Son's age = (2x-5)

According to the Question:

=> (7x-5)(2x-5) = 150

=> 14x²-35x-10x+25 = 150

=> 14x²-45x-125 = 0

=> 14x²-70x+25x-125 = 0

=> (14x²-70x)+(25x-125) = 0

=> 14x(x-5)+25(x-5) = 0

=> (x-5)(14x+25) = 0

Either 14x+25 = 0

=> x = -25/14 (Age can't be negative)

Either (x-5) = 0

=> x = 5

Age of father = 7(5)

= 35

= 35 years

Age of father = 35 years