Discussion

Question:

If 1 is added to the numerator and denominator of a certain fraction, its value becomes 2/3 and if 1 is subtracted from the numerator and denominator of the original fraction, its value becomes 5/8. Find the original fraction.

Explanation:

Let the fraction be x/y.

From the first condition we have,

$\frac{x + 1}{y + 1} = \frac{2}{3}$

∴ 3x – 2y = – 1 … (1)

From the second condition we have,

$\frac{x - 1}{y - 1} = \frac{5}{8}$

∴ 8x – 5y = 3 ... (2)

Solving equation (1) and (2)

⇒ x = 11 and y = 17

∴ The original fraction = 11/17

Hence, option (c).

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