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A man sells two scooters at \[36000\] each. On one scooter he makes \[15\% \] profit and on the other he makes \[15\% \] loss. Find the profit or loss percentage in the whole
A. \[2.25\% \]loss
B. \[2.25\% \]profit
C. \[2.25\% \]loss
D. \[2.25\% \]profit

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Last updated date: 13th Jun 2024
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Answer
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Hint: Assume get of each scooter is \[x\], \[y\] apply the formula of profit \[\% \] and loss \[\% \] we need to get \[x + y\] value then again apply the formula of profit \[\% \] if it is negative then it’s loss otherwise profit.

Complete step-by-step answer:
When we are solving this type of questions, we need to follow the steps
provided in the hint part above.
Let cost price of one scooter is \[x\] then \[profit\% = 15\% \]
At we know that \[profit\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100\]
CP = Cost price
SP = Selling price
\[\begin{array}{l}
 \Rightarrow 15\% = \dfrac{{36000 - x}}{x} \times 100\\
 \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{36000}}{x} - 1\\
 \Rightarrow \dfrac{{36000}}{x} = \dfrac{{15}}{{100}} + 1\\
 \Rightarrow \dfrac{{36000}}{x} = \dfrac{{115}}{{100}}\\
 \Rightarrow x = \dfrac{{3600000}}{{115}}......(1)
\end{array}\]
Now cost price of another scooter is \[y\] apply
\[\begin{array}{l}
loss\% = 15\% \\
loss\% = \dfrac{{C.P - S.P}}{{C.P}} \times 100\\
 \Rightarrow 15 = \dfrac{{y - 36000}}{y} \times 100\\
 \Rightarrow \dfrac{{15}}{{100}} = 1 - \dfrac{{36000}}{y}\\
 \Rightarrow \dfrac{{36000}}{y} = 1 - \dfrac{{15}}{{100}}\\
 \Rightarrow \dfrac{{36000}}{y} = \dfrac{{85}}{{100}}\\
 \Rightarrow y = \dfrac{{3600000}}{{85}}...(2)
\end{array}\]
Now,
\[\begin{array}{l}
x + y = \dfrac{{3600000}}{{115}} + \dfrac{{3600000}}{{85}}\\
x + y = 3600000\left[ {\dfrac{1}{{115}} + \dfrac{1}{{85}}} \right]\\
x + y = 3600000\left[ {\dfrac{{85 + 115}}{{115 \times 85}}} \right]\\
x + y = 368.286 \times [200] = 73657.28
\end{array}\]
Now,
\[\begin{array}{l}
\dfrac{{SP - CP}}{{CP}} \times 100 = ?\\
SP = 2 \times 36000 = 72000
\end{array}\]
Now,
\[\begin{array}{l}
 \Rightarrow \dfrac{{72000 - 73757.28}}{{73757.28}} \times 100\\
 \Rightarrow - 2.25\%
\end{array}\]
Negative means its loss. So, loss of \[2.25\% \].
Hence, option (A) is correct.

So, the correct answer is “Option A”.

Note: In this kind of problems we have to deal with the numerous things and some of them are referenced here which will be truly useful to comprehend the concept:
We have to utilize right formula so as to not turn out to be excessively complex solution:
At the end we need to modify that negative sign means the total selling price will be \[2 \times 36000 = 72000\] not the \[36000\] as there are two scooters.