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Question

A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 12 when 1 is subtracted from the denominator. Find the fraction.

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Solution

Let the numerator of the fraction be x and the denominator be y.

According to the question,

x-2y=13 ...(i) and xy-1=12 ...(ii)Solving equation i, we get3x-2=y3x-6=y ...iiiSubstituting the value of y in equation ii, we getx3x-6-1=122x=3x-6-12x=3x-72x-3x=-7-x=-7x=7 ...(iv)From (iii) and (iv), we getx=7 and y=15Hence, the fraction is 715.

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