Question

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator and 2 to the denominator, the new fraction is 7/11.

Find the original fraction.​

Answer 1

Question.

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator and 2 to the denominator, the new fraction is 7/11.

Find the original fraction.

Answer.

Let denominator of fraction be X.

Numerator = ( X - 8 )

Fraction = Numerator/Denominator = ( X -8)/X.

According to question,

When 1 is added to numerator and 2 is subtracted from denominator the fraction obtained is 2/7.

X - 8 + 1 / X - 2 = 2/7

X - 7 / X - 2 = 2/7

7 ( X - 7 ) = 2 ( X - 2 ).

7X - 49 = 2X - 4.

7X - 2X = -4 + 49

5X = 45

X = 9.

Denominator of fraction = X = 9.

And,

Numerator of fraction = X - 8 = 9-8 = 1.

Fraction = Numerator / Denominator = 1/9