Question

Find a fraction which becomes `(1/2)` when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes `(1/3)` when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

Answer 1

Let the required fraction be `x/y`.
Then, we have:
`(x−1)/(y+2) = 1/2`
⇒ 2(x – 1) = 1(y + 2)
⇒2x – 2 = y + 2
⇒2x – y = 4                   ……(i)
Again,`( x−7)/(y−2) = 1/3`
⇒3(x – 7) = 1(y – 2)

⇒3x – 21 = y – 2
⇒ 3x –y = 19                  ……(ii)
On subtracting (i) from (ii), we get:
x = (19 – 4) = 15
On substituting x = 15 in (i), we get:
2 × 15 – y = 4
⇒ 30 – y = 4
⇒y = 26
∴ x = 15 and y = 26
Hence, the required fraction is `15/26` .