Question

Rohan?s mother is 26 years older than him. The product of their ages (in years)
3 years from now will be 360. We would like to find Rohan?s present age.

Answer 1

Dear student,

Let take Rohan's age = x years

Hence, his mother's age = x + 26

3 years from now

Rohan's age = x + 3

Age of Rohan's mother will = x + 26 + 3 = x + 29

The product of their ages 3 years from now will be 360 so that

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

⇒ x² + 29x + 3x + 87 = 360

⇒ x² + 32x + 87 - 360 = 0

⇒ x² + 32x - 273 = 0.
⇒ x² + (39-7)x - 273 = 0
∴(x+39)(x−7)=0
∴x=−39 and x=7
∴x=7.......(∵ x can not be negative)
∴ Mother's present age=7+26=33


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