Question

A Fraction becomes `1/2` if 5 subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator. Find the fraction.

Answer 1

Let the numerator of the fraction be x and denominator of the fraction be y.
Then, the fraction =`x/y`
According to given condition, we have
`[ x - 5 ]/[ y - 3 ] = 1/2`
⇒ 2x - 10 = y - 3
⇒ 2x - y = 7                               ...(1)
And,
x + 5 = y
⇒ x - y = - 5                             ...(2)
Subtracting (2) from (1), We get
x = 12
⇒ y = x + 5 
⇒ y = 12 + 5 = 17
Hence, the fraction is `12/17`.