# Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. Find Rohan’s present age. A. 9 B. 4 C. 7 D. 1

By BYJU'S Exam Prep

Updated on: September 25th, 2023

To solve the problem, we will focus on Rohan’s age. We are aware of the age difference between Rohan and his mother, so by adding that difference to Rohan’s age, we can determine his mother’s age. Then, we are provided with the product of their ages three years into the future, which can be expressed as a quadratic equation. Our goal is to solve this equation and determine Rohan’s age.

## Calculate Rohan’s Age

Solution:

Let’s consider Rohan’s age to be ‘x’ years.

Hence, his mother’s age would be ‘x + 26’ years.

Three years from now, Rohan’s age would be ‘x + 3’.

His mother’s age would be ‘x + 26 + 3 = x + 29’.

The product of their ages three years from now is given as 360, which gives us the equation:

(x + 3)(x + 29) = 360

Expanding this equation, we get:

x2 + 32x + 87 = 360

Simplifying further:

x2 + 32x – 273 = 0

Factoring the quadratic equation, we have:

(x + 39)(x – 7) = 0

Therefore, either x + 39 = 0 or x – 7 = 0.

If x + 39 = 0, then x = -39, which is not a valid age.

If x – 7 = 0, then x = 7.

Since age cannot be negative, we conclude that Rohan’s age is 7 years.

Therefore, his mother’s age would be 7 + 26 = 33 years.

Summary:

## Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. Find Rohan’s present age.

1. 9
2. 4
3. 7
4. 1

Here, we have calculated that Rohan’s age is 7 years and his mother’s age is 33 years.

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