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If 2 is added to the numerator and 3 is subtracted from the denominator of a fraction, the fraction becomes 3 / 2. If 1 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes 1 / 4. What is the sum of numerator and denominator of that fraction?

If 2 is added to the numerator and 3 is subtracted from the denominator of a fraction, the fraction becomes 3 / 2. If 1 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes 1 / 4. What is the sum of numerator and denominator of that fraction? Correct Answer 11

Calculation:

Let the fraction be x/y

First case,

(x +2)/(y – 3) = 3/2

⇒ 2x + 4 = 3y – 9 → equation 1

Second case,

(x – 1)/(y + 5) = 1/4

⇒ 4x – 4 = y +5 → equation 2

On solving equation 1 and 2, we get

x= 4 and y = 7

∴ the fraction is 4/7 and the sum of numerator and denominator of that fraction = 4 + 7 = 11

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