Your brother is 3 years older than you. Your sister is 4 years younger than you. Th e product of your ages is 1872. How old is your sister?

9 years

Explanation:

let my age be 'x' years

Therefore,

Age of sister = x - 4 years

Age of brother = x + 3 years

Product of ages = 1872

x (x - 4) (x + 3) = 1872

or

x³ - x² - 12x - 1872 = 0

on solving the above cubic equation, we get

x = 13 as the only real root of the equation

Hence,

Age of the sister = x - 4

= 13 - 4

= 9 years