Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

A positive number is increased by 60%60\%. By what percentage should the result be decreased to return to the original value?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Solution 1: Suppose that the original number is 100. When 100 is increased by 60%60\%, the result is 160. To return to the original value of 100, 160 must be decreased by 60. This percentage is 60160×100%=38×100%=37.5%\frac{60}{160} \times 100\%=\frac{3}{8} \times 100\%=37.5\%. Solution 2: Suppose that the original number is xx for some x>0x>0. When xx is increased by 60%60\%, the result is 1.6x1.6x. To return to the original value of xx, 1.6x1.6x must be decreased by 0.6x0.6x. This percentage is 0.6x1.6x×100%=38×100%=37.5%\frac{0.6x}{1.6x} \times 100\%=\frac{3}{8} \times 100\%=37.5\%.

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