Question

The sum of the numerator and the denominator of a fraction is 11. If each of the numerator and denominator is increased by 2 then the fraction becomes 2/3. Find the fraction.

Answer 1

Answer:

the fraction is $\frac{4}{7}$

Step-by-step explanation:

let x & y be the numerator and denominator of the fraction resply.

given that , x + y = 11   => y = 11 - x

also, given that, $\frac{x+2}{y+2}$ = $\frac{2}{3}$

=> $\frac{x+2}{11-x+2}$ = $\frac{2}{3}$

=> 3(x+2) = 2(13-x)

=> 3x+6 = 26-2x

=> 3x+2x = 26-6

=> 5x = 20

=> x = 20/5 = 4

so, y = 11 - 4 = 7

=> the fraction is $\frac{4}{7}$