# Discussion of Question with ID = 023 under Percentages

## This is the discussion forum for this question. If you find any mistakes in the solution, or if you have a better solution, then this is the right place to discuss. A healthy discussion helps all of us, so you are requested to be polite and soft, even if you disagree with the views of others. The question and its current solution has also been given on this page.

### Question

A number is first increased by 80%. By what percent must it be reduced so as to restore it to its previous value?

A

\$44{4/9}\$ %.

B

\$51{1/8}\$ %.

C

\$35{6/11}\$ %.

D

\$38{9/11}\$ %.

Soln.
Ans: a

Let us derive the shortcut formula first, so that you can remember it and use it when the need arises. Suppose the number is 100, and let the increase be x%. The number becomes 100 + x. Let us suppose that it has to be reduced by p% to restore it to 100. Then, (100 + x) - p × \$(100 + x)/100\$ = 100. We can cancel away 100, and easily simplify it to p = \${100 × x}/{100 + x}\$ = \${100 × 80}/{100 + 80}\$ = \${400/9}\$, which is same as: \$44{4/9}\$%.