Question

The sum of the ages of Rohan and his father is 35 years, whereas the product of their ages is 150 .

Assertion (A): Rohan's age is 5 years.

Reason (R): If Rohan's age is x years then x(35 − x) = 150

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Let the age of Rohan be x years.

It is given that the sum of the ages of Rohan and his father is 35 years.

⇒ Father's age = 35 − x

And, the product of their ages is 150.

⇒ x(35 − x) = 150

⇒ 35x − x² = 150

⇒ 35x − x² − 150 = 0

⇒ x² − 35x + 150 = 0

⇒ x² − 30x − 5x + 150 = 0

⇒ x(x − 30) − 5(x − 30) = 0

⇒ (x − 30)(x − 5) = 0

⇒ (x − 30) = 0 or (x − 5) = 0

⇒ x = 30 or x = 5

When son's age is 5 years, father's age = (35 − x) = (35 − 5) = 30 years.

When son's age is 30 years, father's age = (35 − x) = (35 − 30) = 5 years (father's age is less than son's age which is not possible).

So, Assertion (A) and Reason (R) both are true and R is correct reason for A.