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

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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.