Question

If 2 is added to the numerator of a fraction, it reduces to `(1/2) `and if 1 is subtracted from the denominator, it reduces to `(1/3)`. Find the fraction.

Answer 1

Let the required fraction be `x/y`.
Then, we have:
`(x+2)/y = 1/2`
⇒ 2(x + 2) = y
⇒ 2x + 4 = y
⇒2x - y = -4                  ……(i)
Again, `x/(y−1) = 1/3`
⇒3x = 1(y – 1)
⇒3x – y = -1              ……(ii)
On subtracting (i) from (ii), we get:
x = (-1 + 4) = 3
On substituting x = 3 in (i), we get:
2 × 3 – y = -4
⇒ 6 – y = -4
⇒ y = (6 + 4) = 10
∴ x = 3 and y = 10
Hence, the required fraction is `3/10`.