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### Question

A number is first increased by 40%. By what percent must it be reduced so as to restore it to its previous value?

**A**

$28{4/7}$ %.

**B**

$34{1/2}$ %.

**C**

$21{4/9}$ %.

**D**

$24{5/9}$ %.

**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 = ${100 × x}/{100 + x}$ = ${100 × 40}/{100 + 40}$ = ${200/7}$, which is same as: $28{4/7}$%.