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?
Let the required fraction is x/y ATQ: x = y - 2 x - y = -2 ....(i) Also given, y + 3 = 8(x-2) ⇒ y + 3 = 8x – 16 ⇒ 8x – y = 16 + 3 ⇒ 8x – y = 19 …… (ii) Subtracting equation (ii) from (i), we get (x – y) – (8x – y) = – 2 – 19 ⇒ x – y − 8x + y = −21 ⇒ −7x = −21 ⇒ x = 21/7 = 3 Substituting the value of x = 3 in the equation (i) we find y 3 – y = – 2 ⇒ y = 3 + 2 ⇒ y = 5 Therefore, the fraction is 3/5.
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