Question
The sum of numerator and denominator of a fraction is 6
less than twice the denominator. If each of the numerator and denominator is decreased by 2, the fraction becomes 1/3. Find the fraction.Solution
Let the fraction be x/y. According to the first condition: x + y = 2y - 6 => x - y = -6 ...(i) According to the second condition: (x - 2) / (y - 2) = 1/3 => 3(x - 2) = 1(y - 2) => 3x - 6 = y - 2 => 3x - y = 4 ...(ii) Subtract equation (i) from (ii): (3x - y) - (x - y) = 4 - (-6) 2x = 10 => x = 5 Substitute x=5 in (i): 5 - y = -6 => y = 11 The fraction is 5/11.
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