Question

A number is mistakenly divided by $5$ instead of being multiplied by $5$. Find the percentage change in the result due to this mistake.
A. $96\% $
B. $95\% $
C. $2400\% $
D. $200\% $
E. None of these

Answer 1

Hint: Always find out the difference between the two numbers when you are comparing, divide the resultant by the original number and multiply with $100\% $
Percentage change $ = \dfrac{{difference}}{{Originalnumber}} \times 100$

Complete step by step solution:Given that number is mistakenly divided by $5$
Therefore, the actual number would be $ = 5x$
But by mistake, the number was divided by $5$
Therefore, the number would be $ = \dfrac{x}{5}$
Now, take the difference between the Actual number and the mistaken number.
$\therefore Difference{\rm{ = 5x - }}\dfrac{x}{5}$
$\begin{array}{l}
 = \dfrac{{25x - x}}{5}\\
 = \dfrac{{24x}}{5}
\end{array}$
Substitute the values of difference and actual number in the formula-
Percentage change $ = \dfrac{{difference}}{{ActualNumber}} \times 100$
Percentage change $ = \dfrac{{24x/5}}{{5x}} \times 100$
Simplify the above equation-
(taking “X” common from the numerator and denominator”)
Percentage change $ = \dfrac{{24}}{{25}} \times 100$
Percentage Change
$\begin{array}{l}
 = 24 \times 4\\
 = 96\%
\end{array}$
Therefore, the required solution is -
The percentage change in the result due to this mistake is $96\% $
Hence, from the given multiple choices, option A is the correct answer.

Note: One can also solve the same question by the alternative method. By using formula-
Percentage Increase /Decrease = $\dfrac{{Original{\rm{ number - old}}\;{\rm{number}}}}{{Original{\rm{ number}}}} \times 100$. Always remember that numerators can never be zero or negative numbers. It is always the positive number.