If the numerator of a fraction is increased by 2 and the denominator is increased by 1, the fraction because 5/8 and if the numerator of the same fraction is increased by 3 and the denominator is increased by 1, the fraction becomes 3/4 . What is the original fraction?

Data inadequate
2/7
4/7
3/7

Correct Answer: 3/7

Explanation:

Let the original fraction be p/q
Then, (p + 2) / (q + 1) = 5/8
⇒ 8p - 5q = 11 .....(i)
Again (p + 3) / (q + 1) = 3/4
⇒ 4p - 3q = 9 ...(ii)
Solving equations , (i) and (ii), we get ,
p = 3 and q = 7
∴ Fraction = 3/7

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