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If a fraction's numerator is increased by 1 and the denominator is increased by 1 and denominator is increased by 2 then the fraction becomes 2/3. But when the numerator is increased by 5 and the denominator is increased by 1, then the fraction becomes 5/4. What is the value of the original fraction ?
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- 3/7
- 5/8
- 5/7
- 6/7
Correct Option: C
Let the numerator and denominator be p and q respectively.
Then, (p + 2) / (q + 3) = 7/9
⇒ 9(p + 2) = 7(q +3)
⇒ 9p - 7q = 3 ....(i)
Again, (p - 1) / (q - 1) = 4/5
⇒ 5p - 4q = 1 ....(ii)
Solving (i) and (ii) we get,
p = 5, q = 6
Required fraction = 5/6
