Question

There is a fraction such that if 3 is added to the numerator, its value will be 1/3, and if 7 is subtracted from the denominator, its value will be 1/5. What is the fraction? Give the answer in the form of a fraction.

Answer 1

`1/12`

Explanation:

`f = n/d`
`(n+3)/d = 1/3 => n = d/3 - 3`
`n/(d-7) = 1/5 => n = d/5 - 7/5`
`=> d/3 - 3 = d/5 - 7/5`
`=> 5 d - 45 = 3 d - 21" (multiplying both sides with 15)"`
`=> 2 d = 24`
`=> d = 12`
`=> n = 1`
`=> f = 1/12`