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 ratio 2:3 find the fraction

Answer 1

Let the numerator be x and denominator be y
Ist condition
(x+y)=4+2x

IInd condition
x+3/y+3=2:3
x+3/y+3=2/3
3(x+3)=2(y+3)
3x+9=2y+6
3x-2y=6-9
3x-2y= -3
-2y= -3-3x
-y= -3-3x/2
-y= -(3+3x)/2
y=3+3x/2----------(1)


Put the value of (1) in Ist condition(
(x+y)=4+2x
(x+3+3x/2)=4+2x
2x+3+3x/2=4+2x
5x+3/2=4+2x
5x/2+3/2=4+2x
5x/2-2x=4-3/2
5x-4x/2=8-3/2
x/2=5/2
2x=10
x=5

(x+y)=4+2x
5+y=4+2*5
5+y=4+10
y=14-5
y=9

the fraction is 5/9

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