Question

A number is first increased by 20% and then decreased by 20%. What is the net increase or decrease percent?

Answer 1

A number, suppose $x$, is increased by 20% and then decreased by 20%.

It is increased by 20%.

20% of $x$ = $x*20$% = $x* \frac{20}{100}$

= $\frac{20x}{100}$

= $\frac{x}{5}$

After increasing by $20$%, the total amount is =

= $x+20$% of $x$                           

= $x+\frac{x}{5}$                           

= $\frac{5x+x}{5}$                            

= $\frac{6x}{5}$  


Now, number is $\frac{6x}{5}$.

$\frac{6x}{5}$ will be decreased by $20$% of $\frac{6x}{5}$ .


20% of $\frac{6x}{5}$ = $20$% of $\frac{6x}{5}$

= $\frac{6x}{5}*20$%

= $6x*4$%

= $24x$%

= $\frac{24x}{100}$

∴ $\frac{6x}{25}$


After decreasing by $20$%, the total amount is =

= $\frac{6x}{5}-\frac{6x}{25}$

= $\frac{5(6x)-6x}{25}$

= $\frac{30x-6x}{25}$

= $\frac{24x}{25}$

So, net decrease amount is...

$x- \frac{24x}{25}$

= $\frac{25x-24x}{25}$

= $\frac{x}{25}$

The net decrease percentage = 

= $\frac{x}{25}*100$%

= $x*4$%

= $4$%

ANSWER: The net decrease percentage is 4%.

Answer 2

Answer:

I have came here to check answer ....