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### Question

A number is first increased by 60%, and thereafter it is reduced by 60% again. What is the overall reduction?

**A**

36 %.

**B**

38 %.

**C**

34 %.

**D**

40 %.

**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. When it is reduced by x%, we get 100 + x - $((100 + x) × x)/100$ = 100 + x - $(x + x^2/100)$ = 100 - $x^2/100$, hence a reduction of $x^2/100$ = 36%