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