Question
The numerator of a fraction is 2 less than its
denominator. If the numerator is decreased by 2 and the denominator is increased by 3, the denominator becomes eight times the numerator. Find the fraction?ΒSolution
Let the required fraction is x/y ATQ: x = y - 2 x - y = -2 ....(i) Also given, y + 3 = 8(x-2) β y + 3 = 8x β 16 β 8x β y = 16 + 3 β 8x β y = 19 β¦β¦ (ii) Subtracting equation (ii) from (i), we get (x β y) β (8x β y) = β 2 β 19 β x β y β 8x + y = β21 β β7x = β21 β x = 21/7 = 3 Substituting the value of x = 3 in the equation (i) we find y 3 β y = β 2 β y = 3 + 2 β y = 5 Therefore, the fraction is 3/5.
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