Name: % from Ratios and Decimals to % and vice versa
Uploaded: 2019-07-19
Duration: 5 min 7 s
Description: This video discusses Percentages from Ratios, Conversion of Decimals to percentages,Conversion of percentages to Decimals. These conversions are useful to solve % problems.

Question

A number is increased by

10 %

and the increased number is decreased by

10 %

. Show that the net decrease is

1 % .

Accepted Answer

Given that a number is increased by $10 %$ and the increased number is decreased by $10 %$ .

We are asked to show that the net decrease is $1 % .$

Let $x$ be the number.

The number is increased by $10 % .$

Increased number $= (100 + 10) % of x$

$= 110 % of x$

$= \frac{110}{100} \times x$

$= \frac{11 x}{10}$

Then, the number is decreased by $10 % .$

Decreased number $= (100 - 10) % of \frac{11 x}{10}$

$= 90 % of \frac{11 x}{10}$

$= \frac{90}{100} \times \frac{11 x}{10}$

$= \frac{9 \times 11 x}{100}$

$= \frac{99 x}{100}$

$∴$ The net decrease $= x - \frac{99 x}{100}$

$= \frac{(100 x - 99 x)}{100}$

$= \frac{x}{100}$

Hence, the net percentage decrease $= \frac{Net decrease}{Original number} \times 100 %$

$= \frac{\frac{x}{100}}{x} \times 100 %$

$= \frac{x}{100} \times \frac{1}{x} \times 100 %$

$= 1 %$

Hence, showed that the net decrease is $1 %$ .

A number is increased by $10 %$ and the increased number is decreased by $10 %$ . Show that the net decrease is $1 % .$

Important Questions on Percentage

Learn and Prepare for any exam you want !

A number is increased by 10% and the increased number is decreased by 10%. Show that the net decrease is 1%.

Important Questions on Percentage

Learn and Prepare for any exam you want !

A number is increased by $10 %$ and the increased number is decreased by $10 %$ . Show that the net decrease is $1 % .$