Question

. A number is first increased by 20% and the

resulting number is then decreased by 10%.
Find the overall change in the number as
percent.
​

Answer 1

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A number :

`x`

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20% of it :

`(20)/(100)x = (2)/(10) x = 0.2x \\`

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A number increased by 20 % , thus :

`x + 0.2x = 1.2x`

This is the resulting number.

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10% of resulting number :

`(10)/(100) * 1.2x = (1)/(10) * 1.2x = \\`

`0.1 * 1.2x = 0.12x`

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The resulting number decreased by 10% ; So :

`1.2x - 0.12x = (1.20 - 0.12)x = \\`

`1.08x`

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`1.08x = 1x + 0.08x = x + 0.08x \\`

Thus the overall change in the number as percent is :

`0.08 * 100 = (8)/(100) * 100 = 8 \: percent \: \: increasing \\`

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