Question

A number is mistakenly divided by 10 instead of being multiplied by 10. Find the percentage change in the result due to this mistake.
1. -99%
2. +99%
3. -100%
4. +100%

Answer 1

Hint: In this question, we have to find the percentage of change. So, we will assume the number to be ‘x’. To find the change between two numbers we will find the difference between two numbers and divide it by the original number and multiply it by 100.

Complete step-by-step solution:
Let the number be ‘x’.
So, the actual number would be $$10x$$.
It is said that the number is mistakenly divided by 10. So, the number would be ${\displaystyle \frac{x}{10}}$.
To find the percentage first we will find the difference between the actual number and the mistaken number.
$={\displaystyle \frac{x}{10}}-10x$
Now we will take the L.C.M. of the denominator.
$={\displaystyle \frac{x-100x}{10}}$
$={\displaystyle \frac{-99x}{10}}$
Now, we will find the percentage change using the formula ${\displaystyle \frac{\text{difference}}{\text{actual number}}}\times 100$.
Substituting the values in the formula,
$={\displaystyle \frac{{\displaystyle \frac{-99x}{10}}}{10x}}\times 100$
$={\displaystyle \frac{-99x}{100x}}\times 100$
$={\displaystyle \frac{-99x}{x}}$
$=-99\mathrm{\%}$
The percentage change in the result is -99%.
So, option (1) is the correct answer.

Note: A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol ‘%’.
The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
$$\mathrm{\%}\text{increase = }{\displaystyle \frac{\text{(new number - actual number)}}{\text{actual number}}}\times 100$$
where,
increase in number = New number – actual number
Similarly, percentage decrease is equal to subtraction of new number from original number, divided by original number and multiplied by 100.
$$\mathrm{\%}\text{decrease = }{\displaystyle \frac{\text{(actual number - new number)}}{\text{actual number}}}\times 100$$
Where decrease in number = Actual number – New number
So, basically if the answer is negative then there is a percentage decrease.