# 一條難度十分高的英文百分數題

Peter claims that when a number x is increased by 10% and then decreased by 10%, the value of x is unchanged.

His calculation: x(1 + 10% - 10%) = x

Peter os wrong. Point out the mistake.

### 5 個解答

• 1 十年前
最愛解答

The equation should be

X (1+10%) (1-10%) = X

The question means increment by 10% is X (1+10%) &lt;= New amount

Then the increased amount decrease by 10%, i.e. the new amount times (1-10%)

So, it should be X (110%) (90%) =X

Then, 99% X = X

X seems equal to &quot;0&quot;

• 1 十年前

Peter&#39;s calculation is wrong. The right method is as follows:

new value of X = (1+10%) (1-10%) X

= (1.1) (0.9) X

= 0.99X

Therefore, new value of X should become less.

資料來源： myself
• 1 十年前

x is increased by 10% ------&gt;(1+10%)x = 1.1x

then decreased by 10%----&gt; (1-10%)* 1.1x

-----&gt;0.99x

• Thomas
Lv 6
1 十年前

When a number x is increased by 10%, it becomes 1.1x

And then decreased by 10%, it becomes 0.99x

The value of x has been decreased by 1%

His mistake is that the formula should be

x (1+10%)(1-10%) instead of x(1 + 10% - 10%)

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• 1 十年前

100% + 10% = 110%

110% * 0.9 = 99%

X went down from 100% to 99%