Question

15. The numerator of a 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 2/3Find the original fraction.
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Answer 1

let the numerator be x-7 and denominator be x

according to the question

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

x-4/2+x = 2/3

2(2+x) = 3(x-4)

4+2x = 3x-12

2x-3x = -12-4

-x = -16

x = 16

hence, numerator = 16-7 = 9

denominator = 16