Question

the numerator of a fraction is 3 less than the denominator. if both the numerator and denominator are increased by 2 , the new fraction becomes 6\7 . find the original fraction

Answer 1

Hey

Here is your answer,

Let the denominator of the fraction be X.
Then the numerator of the fraction = (X-3)
Fraction = Numerator/Denominator = X-3/X.

Numerator and denominator are increased by 2 then the Numerator and denominator becomes (X-3+2) and (X+2).

Fraction = Numerator/Denominator =(X-3+2)/(X+2).

According to question,

(X-3+2)/(X+2) = 6/7
X-1/X+2 = 6/7
7(X-1) = 6(X+2)
7X-7 = 6X+12
7X-6X= 12+7
X = 19

Numerator = (X-3) = (19-3) = 16
Denominator =(X) = 19

Therefore,
Original Fraction = Numerator/Denominator = (X-3)/X= 19/16

Hope it helps you!