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 option 1. A is true, R is false. 2. A is false, R is true. 3. Both A and R are true and R is correct reason for R. 4. Both A and R are true and R is incorrect reason for R.

Mathematics

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

Reason

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.

Hence, option 3 is the correct option.

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