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If the numerator of a fraction is increased by 2 and denominator is increased by 3, the faction becomes 7/9 and if numerator as well as denominator are decreased by 1, the fraction becomes 4/5. What is the original fraction ?
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- 13/16
- 9/11
- 5/6
- 17/21
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
