Question

By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?

Answer 1

80% increase

Explanation:

let the given fraction
`f=(x)/(y)`

numerator=
`x`

denominator=
`y`

Given

• numerator decreased by 10%
• denominator decreased by 50%

let new numerator
`=x_(new)=x-(10)/(100) x=(9)/(10) x`

let new denominator
`=y_(new)=y-(50)/(100) y=(1)/(2) y`

Therefore new fraction,
`f_(new)=(x_(new) )/(y_(new) )=((9)/(10)x)/((1)/(2)y )=(9*2)/(10) (x)/(y)=(9)/(5) (x)/(y)`

Percentage increase
`=(f_(new) -f)/(f) * 100=((9)/(5) (x)/(y) -(x)/(y) )/((x)/(y) )* 100=(4)/(5) *100= 80`

⇒ Percentage increase of function
`f` = 80%