# If we increace by 25% how much % we have to decrease to get back to original value

I am currently stuck at a problem where i have to add 25% to the original value and then i have to answer how much % I have to devide from the new value to get original value. I tried percent proportion but it seems to not work and i cant think of any other method to get the answer. Could someone please put me on the right track, I dont need the answer I just need for you to point me on a right track to get this answer.

to increase by $25$% you multiply by $1.25$

So in reverse you multiply by $\frac{1}{1.25}=0.8$

Hint:

If $a$ is the inital value, an increment of $s\%$ gives the new value $b=a(1+s\%)$. You want a decrement $t\%$ such that: $$b(1-t\%)=a$$ so you have the equation: $$a(1+s\%)(1-t\%)=a \iff (1+s\%)(1-t\%)=1$$

can you solve in your case?

Suppose the original value is $X$.

Then the new value, $Y$, is $Y = X + 0.25X$. That is, add $X$ and $25\%$ of $X$.

Now $X+0.25X = 1X+0.25X = 1.25X$.

So $Y = 1.25X$.

To solve for the old value, we are looking for $X$, so divide by $1.25$: $X = \dfrac{Y}{1.25}$.

Suppose the quantity is 100. So after 25% increase, you have 125. All you need to figure out is what percentage of 125 is 25.

The equation to evaluate will be $$\frac{100x}{125}=25$$

Hope it helps.

you have to decrease by 20%.

Suppose you had 100 at beginning after increasing it will be 125.

you have decrease it by 25 to get back to the original 100.

that is you have to decrease $\frac{25}{125} 100 \% = 20 \%$