Question

1) The sum of numerator and denominator of a fraction is greater by 1
than thrice the numerator. If the numerator is decreased by 1/3 then the
fraction reduces to
}.
Find the fraction.
​

Answer 1

Let a/b represent the fraction.

(a+1)/(b+1) = 2/3

(a–2)/(b-2) = 1/3

Cross-multiplying, we have:

3a+3 = 2b+2

3a–6 = b-2

Now, subtract the second equation from the first:

9 = b+4

or

b= 5

If 3a–6 = b-2, then 3a–6 = 5-2 = 3, so 3a = 9 and a=3.

Therefore, the fraction is 3/5.

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