Question

If the numerator of a fraction increase by 1 it's values becomes 3/4. If it denominator is increase by 2 its value becomes 1/2 find the fraction

Answer 1

let numertor be x
denominator be y
then the fraction is
$\frac{x}{y}$
$\frac{x + 1}{y} = \frac{3}{4} \\ 4(x + 1) = 3y \\4x + 4 = 3y \\ 4x - 3y = - 4 \: eq.(1)\\ \frac{x}{y + 2} = \frac{1}{2} \\ 2x = y + 2 \\ 2x - y = 2 \: eq.(2) \\ now \: mutliply \: eq1 \: with \: 2 \: and \: eq2 \: with \: 4 \\ we \: get \\ 8x - 6y = - 8 \: \: eq3 \\ 8x - 4y = 4 \: \: eq4 \\ substracting \:eq \: 4 \: \: from \: 3 \\ - 2y = - 12 \\ y = 6 \\ put \: value \: of \: y \: in \: eq \: 4 \\ 8x - 4(6) = 4 \\ x = \frac{7}{2} \\ mutiply \: x \: y \: with \: 2 \\ \frac{x}{y} = \frac{7}{12}$

Answer 2

let assume X is numerator

and let assume Y is denominator

and fraction will become like this numerator/denominator

fraction=a

X+1/Y=3/4

4X+4=3Y

4X-3Y=-4 A

X/(Y+2)=1/2

2X=Y+2

2X-Y=2B

Now multiply equation A with 2 and B with 4

8X-6Y=-8 C

8X-4Y=8 D

Subtract equation D from C,

-2Y=-16

Y=8

Put Y=8 in equation D)

8X-4(8)=8

8X-32=8

8X=40

X=5

Numerator X=5

Denominator y=8

X/Y=5/8