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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 wholeA. $2.25\%$lossB. $2.25\%$profitC. $2.25\%$lossD. $2.25\%$profit

Last updated date: 13th Jun 2024
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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.

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.