Question

A fraction becomes 9/11,if2is added to both the numerator and the deminator. if 3 is added to both the numerator and the deminator it becomes 5/6. Find the fraction​

Answer 1

Answer

Let the fraction be x/y

According to the question

$\rm \frac{x+2}{y+2} = \frac{9}{11}$

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

=> 11x + 22 = 9y + 18

=> 11x - 9y = -4 ---->(1)

And,

$\rm \frac{x+3}{y+3} = \frac{5}{6}$

=> 6(x+3) = 5(y+3)

=> 6x + 18 = 5y + 15

=> 6x - 5y = -3 ---->(2)

Multiplying (1) by 6 and (2) by 11, we get:

6(11x - 9y = -4)

=> 66x - 54y = -24 ---->(3)

And,

11(6x - 5y = -3)

=> 66x - 55y = -33 ---->(4)

By elimination method

Subtracting (3) from (4) we get:

y = 9

from (2) we have: 6x - 5y = -3

=> 6x - 5(9) = -3

=> 6x - 45 = -3

=> 6x = 42

=> x = 7

Therefore, the fraction is $\large \rm \frac{7}{9}$

Answer 2

Answer:

we assume that numerator is x and denomentor is y

ATQ. X+2/y+2=9/11 ,,

by multiplication method 11x+22=9y+18

11x-9y=18-22

11x-9y= -4____(1)

X+3/y+3=5/6,,

by multiplication method 6x+18=5y+15

6x-5y = 15-18

6x-5y = -3

X=5y-3/6 _____(2)

Step-by-step explanation:

put 2nd equation in 1st equation

11(5y-3/6)-9y = -4

11(5y-3)-54y = -24

y=33-24 = 9 ans.

Put y value in equation 2nd

6x - 5(9) = -3

6x = 45-3

6x = 42

X= 42/6

X= 7.ans.

fraction will be 7/9