Question

The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is 11/30. Find the fraction.

Answer 1

The answer is given below :

Let the denominator be x.
So, numerator be (x + 1).

Then the number is (x + 1)/x.

Reciprocal of this number is x/(x + 1).

Given,

(x + 1)/x - x/(x + 1) = 11/30

=> 30 [(x + 1)² - x²] = 11 [x(x + 1)]

=> 30 (x² + 2x + 1 - x²) = 11x² + 11x

=> 60x + 30 = 11x² + 11x

=> 11x² - 49x - 30 = 0

=> 11x² - 55x + 6x - 30 = 0

=> 11x(x - 5) + 6(x - 5) = 0

=> (x - 5)(11x + 6) = 0

So, either x - 5 = 0 or, 11x + 6 = 0

=> x = 5 or, x = -6/11

When, x = 5,

the fraction is = (5 + 1)/5 = 6/5

When, x = -6/11,

the fraction is = (-6/11 + 1)/(-6/11) = 5/(-6), which does not fulfil the given conditions.

Thus the required fraction = 6/5.

Thank you for your question.