Question
The numerator of a fraction is increased by 10% and the
denominator is decreased by 30%. If the new fraction exceeds the original fraction by (1/2), find the original fraction.Solution
ATQ, Let original fraction be x/y New numerator = (110/100)x = (11/10)x New denominator = (70/100)y = (7/10)y So, new fraction = [(11/10)x]/[(7/10)y] = (11x/10) × (10/7y) = 11x/7y ATQ, (11x/7y) − (1/2) = (x/y) Or, (11x/7y) − (x/y) = 1/2 Or, (11x/7y) − (7x/7y) = 1/2 Or, 4x/7y = 1/2 Or, x/y = 7/8 Therefore, original fraction = 7/8
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