Question

The ages of the two sisters are 11 years and 14 years. In how many years time will the product of their ages be 304?

Answer 1

Given : The ages of two sisters are 11 and 14 years

Suppose in x years the product of their ages becomes 304

Now, according to question,

( 11 + x ) ( 14 + x ) = 304

154 + 11x + 14x + x² = 304

x² + 25x - 150 = 0

x² + 30x - 5x - 150 = 0

x ( x + 30 ) - 5 ( x + 30 ) = 0

( x + 30 ) ( x - 5 ) = 0

So,

x = 5 and - 30

But time (in years) can't be negative , So we neglect x = - 30

We get

x = 5

So,
After 5 years product of their ages is 304