The number was reduced by p%, the resulting number was reduced again by q%.

The number was reduced by p%, the resulting number was reduced again by q%. How much the number was reduced if a) p = 20, q-20. b) p = 30, q = 40

Let X be a given number. We decrease the number by p%. It was 100%, it is now (100 – p)%. But you cannot operate with percentages, let’s convert the percentages to a decimal number, for this we divide by 100%: (100 – p) / 100.

This means that you get a number equal to x * (100 – p) / 100.

Reduce the number by another q%: (100 – q) / 100.

The result is the number x * (100 – p) / 100 * (100 – q) / 100.

a) p = 20, q = 20.

Substitute in the expression:

x * (100 – 20) / 100 * (100 – 20) / 100 = x * 80/100 * 80/100 = x * 0.8 * 0.8 = 0.64 * x.

Let’s convert the decimal number back to percent: 0.64 = 64%.

That is, the resulting number is 64% of the number x, that is, the number has decreased by 36% (100 – 64 = 36).

b) p = 30, q = 40.

x * (100 – 30) / 100 * (100 – 40) / 100 = x * 70/100 * 60/100 = x * 0.7 * 0.6 = 0.42x.

0.42 = 42%.

This means that the number has decreased by 58% (100 – 42 = 58).