Question

If a number is increased by 25% and then decreased by 25%, find out thepercentage of increase/decrease of final value of the number.​

Answer 1

Answer:

37.5%

Step-by-step explanation:

Let the number be x.

The increased no.

= x + 25% of x

$= x + \frac{25}{100} \times x$

$= x + \frac{x}{4}$

$= \frac{5x}{4}$

Now,

The decreased no.

$= \frac{5x}{4} - 25\% \: of \: \frac{5x}{4}$

$= \frac{5x}{4} - \frac{1}{4} \times \frac{5x}{4}$

$= \frac{5x}{4} - \frac{5x}{8}$

$= \frac{10x - 5x}{8}$

$= \frac{5x}{8}$

The required percentage

$= ( \frac{x - \frac{5x}{8}}{x} \times 100)\%$

$= (\frac{ \frac{8x - 5x}{8} }{x} \times 100)\%$

$= ( \frac{ \frac{3x}{8} }{x} \times 100 )\%$

$= ( \frac{3x}{8} \times \frac{1}{x} \times 100)\%$

$= ( \frac{300}{8} )\%$

= 37.5%

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