## a fraction becomes 9/11 if 2 is added to both the numerator and the denominator.if 3 is added to both the numerator and the denominator it

Question

a fraction becomes 9/11 if 2 is added to both the numerator and the denominator.if 3 is added to both the numerator and the denominator it becomes 5/6. find the fraction.​

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4 days 2021-10-10T07:29:14+00:00 2 Answers 0 views 0

fraction = 7 / 9

## Solution

Let numerator be = x

Let denominator be = y

so Fraction is = x / y

## Given

If two is added to both numerator and

denominator

x + 2 / y + 2 = 9 / 11

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

11x + 22 = 9y + 18

11x – 9y + 4 = 0 …… (1)

## Given

If 3 is added both numerator and

denominator

x + 3 / y + 3 = 5 / 6

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

6x + 18 = 5y + 15

6x – 5y + 3 = 0 …….. ( 2)

EQUATION =

11x – 9y + 4 = 0 ….. (1)

6x – 5y + 3 = 0 …… (2)

from equation (1) and equation (2) we get

x = 7

put x = 7 in equation (2)

6 ( 7 ) – 5y + 3 = 0

45 – 5y = 0

y = 9

therefore,

Numerator = x = 7

Denominator = y = 9

Hence, fraction is = 7 / 9 = ANSWER