Question

The numerator of the fraction is 7 less than the denominator. If 3 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 2/3
, Find the original fraction.

Answer 1

Let numerator be x.

Denominator is x+7.

If,

x+3/x+7+2 = 2/3

x+3/x+9 = 2/3

3(x+3) = 2(x+9)

3x+9 = 2x+18

3x- 2x =18-9

x = 9

x+7 = 9+7

= 16

Hence, original fraction is 9/16.

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Answer 2

Answer:

Let the numerator be x and

the denominator be y

Given that numerator of a fraction is 7 less than its denominator

Therefore, x+7=y ------(1)

Given that if the denominator increased by 9 and the numerator by 2 then the fraction is 2/3

Therefore, X+2/y+9 = 2/3

⟹3x+6=2y+18

⟹3x−2y=12

⟹3x−2(x+7)=12

⟹x−14=12

⟹x=26

⟹y=26+7=33 (from (1))

Therefore, the fraction is 26/33