Take the number 700. Increase it by 60%, then decrease the result by 60%. What is the final resulting number?

Take the number 700. Increase it by 60%, then decrease the result by 60%. What is the final resulting number?

700*1,6 = 1120;  1120*0,4 = 448

So the answer is 448.

We observe that:

x(1+y)(1-y) = x(1 -y²)

x(1+0,01y)(1-0,01y) = x(1 - 0,0001y²) = x(1 - 0,01*y²)

So, if you increase a number by y %, and the decrease it by y %, you, in effect, decrease the number by 0,01*y² %.

The original number is 700.

To increase it by 60%: find 60% of 700 and add this amount to 700:

     60% of 700   ===>   .60 x 700  =  420

     adding this to 700, the total is now 1120.

To decrease this amount by 60%: find 60% of 1120 and subtract this amount from 1120:

     60% of 1120   ===>   .60 x 1120  =  672

     subtracting this from 1120, the final amount is 448.

Increasing an amount by a certain percentage and then decreasing that amount by the same percentage results in a smaller answer than what you started with because the amount that you subtract is more than what you add. 

When increasing a number by a percentage, you essentially find 100% + the percentage. In this case, 100%+60%=160%. As a decimal, this would be 1.6.

So

$${\mathtt{700}}{\mathtt{\,\times\,}}{\mathtt{1.6}} = {\mathtt{1\,120}}$$

This is 700 increased by 60%

When you decrease a number by a percentage, you are finding 100%-percentage decrease. In this case 100%-60%=40%. As a decimal this would be 0.4

So

$${\mathtt{1\,120}}{\mathtt{\,\times\,}}{\mathtt{0.4}} = {\mathtt{448}}$$