Question

Last year , there were 30 male members and 20 female members in a Chess Club . This year , the number of male members is decreased by r% while the number of female members is increased by r% . If the number of male members is equal to that of female members this year , find the value of r .

Can anyone explain to me ?
Thks \（>∀<）/

Answer 1

The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

`30*\cfrac{r}{100} = 0.3 r`

and similarly, the r% of female is

`20*\cfrac{r}{100} = 0.2 r`

The number of males decreased by this quantity, so now it is

`30 - 0.3r`

and the number of female increased by this quantity, so now it is

`20+0.2r`

we know that these two new counts are the same number, so we can build and solve the equality

`30 - 0.3r = 20+0.2r`

Subtract 20 and add 0.3r from both sides:

`10 = 0.5r`

Divide both sides by 0.5 to solve for r:

`r = 20`

Let's check the answer

The 20% of 30 is
`30 * (20)/(100) = 6`, while the 20% of 20 is 4. So, we are stating that
`30-6 = 20+4` which is true because both expressions evaluate to 24.