Question

If the numerator and denominator of the fraction is increased by 2an1 respectively; it becomes3/4 if the numerator and the denominator are decreased by 2and1 respectively , it becomes 1/2. Find the fraction

Answer 1

Answer:

The fraction is$\frac{7}{1}$

Step-by-step explanation:

Let the numerator be x and denominator be y

So, Fraction = $\frac{x}{y}$

Now we are given that numerator and denominator of the fraction is increased by 2 and 1 respectively. it becomes 3/4

So, Fraction becomes :$\frac{x+2}{y+1}=\frac{3}{4}$

$4(x+2)=3(y+1)$

$4x+8=3y+3$

$4x-3y+5=0$----1

We are also given that the numerator and the denominator are decreased by 2 and 1 respectively , it becomes 1/2

So, Fraction becomes :$\frac{x-2}{y-1}=\frac{1}{2}$

$2(x-2)=y-1$

$2x-4=y-1$

$2x-y-3=0$ ---- 2

Substitute the value of y from 2 in 1

$4x-3(2x-3)+5=0$

$4x-6x+9+5=0$

$14=2x$

$7=x$

Substitute the value of x in 2

$2(2)-y-3=0$

$4-3=y$

$1=y$

So, Fraction = $\frac{x}{y}=\frac{7}{1}$

Hence The fraction is$\frac{7}{1}$