Question

The sum of numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3. Find the fraction.

Answer 1

ANSWER: 5/9

EXPLANATION-


let the numerator be x and denominator be y
x+y=4+2x

y=4+2x-x

y=4+x

y-x=4

-x+y=4...(1)

x+3/y+3=2/3

3(x+3)=2(y+3)

3x+9=2y+6

3x-2y=6-9

3x-2y=-3....(2)

multiplying (1) by 2

-x+y=4...(1)
-2x+2y=8
adding

3x-2y=-3....(2)
-2x+2y=8
x=5

-x+y=4
-5+y=4
y=4+5
y=9

hence the fraction is
$\frac{5}{9}$

hope this helps you :-)