Question
A fraction becomes 6/7 when 3 is
added to both its numerator and denominator. Similarly, it becomes 7/8 when 5 is added to both its numerator and denominator. Determine the original fraction.Solution
ATQ, Let the original fraction be (x/y). {(x + 3)/(y + 3)} = (6/7) Or, 7x + 21 = 6y + 18 Or, 6y – 7x = 3 -------- (I) Also, {(x + 5)/(y + 5)} = (7/8) Or, 8x + 40 = 7y + 35 Or, 7y – 8x = 5 --------- (II) Equation (I) × 7 - Equation (II) × 6, we get 42y – 49x – 42y + 48x = 21 – 30 Or, x = 9 Putting ‘x’ in equation (I), we get y = (3 + 7 × 9)/6 = 11 so, the fraction = (9/11)
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