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Question

Answers

A. $96\% $

B. $95\% $

C. $2400\% $

D. $200\% $

E. None of these

Answer

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Percentage change $ = \dfrac{{difference}}{{Originalnumber}} \times 100$

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.

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.