Question

A fraction becomes 911if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 56. Find the fraction.

Answer 1

Step-by-step explanation:

Let the fraction will be X and Y. According to the question/

(x+2)/(y+2)=9/11

or, 11x+22=9y+18

or, 11x-9y=18-22

or, 11x-9y=-4

or, 11x=9y-4

or, x=(9y-4)/11

and, (x+3)/(y+3)=5/6

then, x=(9×9-4)/11

then, x=(9×9-4)/11or, x=(81-4)/11

then, x=(9×9-4)/11or, x=(81-4)/11or, x=77/11=7

so x=7,y=9 and the fraction is :7/9

Answer 2

$\huge\bigstar\mathfrak\blue{\underline{\underline{SOLUTION:}}}$

Let the numerator of the fraction be x

Let the numerator of the fraction be x & its denominator be y.

Fraction=

$\frac{x}{y}$

Case 1️⃣

When 2 is added to both numerator & denominator,then

$\frac{x + 2}{y + 2} = \frac{9}{11} \\ \\ = > 11x + 22 = 9y + 18 \\ \\ = > 11x = 9y - 4............(1)$

Case 2️⃣

When 3 is added to both numerator & denominator, then

$\frac{x + 3}{y + 3} = \frac{5}{6} \\ \\ = > 6x + 18 = 5y + 15 \\ = > 6x = 5y - 3 \\ = > x = \frac{5y - 3}{6} ...........(2)$

On putting value of x in (1), we get

$= > 11( \frac{5y - 3}{6} ) = 9y - 4 \\ \\ = > 11(5y - 3) = 54y - 24 \\ = > 55y - 33 = 54y - 24 \\ = > 55y - 54y = - 24 + 33 \\ = > y = 9$

On putting y in equation (2), we get

$x = \frac{5 \times 9 - 3}{6} \\ \\ = > x = \frac{42}{6} = 7$

So, the required fraction

$= > \frac{x}{y} = \frac{7}{9}$

hope it helps ☺️