Discussion of Question with ID = 023 under Percentages

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


$44{4/9}$ %.


$51{1/8}$ %.


$35{6/11}$ %.


$38{9/11}$ %.

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: $44{4/9}$%.

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