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# Amina buys a book for Rs. 275 and sells it at a loss of 15 %. By how much does she sell it for(a) Rs. 230(b) Rs. 233.75(c) Rs. 240(d) Rs. 245

Last updated date: 12th Jul 2024
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Answer
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Hint: Here, we have to evaluate the selling price. The selling price is given as SP = CP – Loss. So, firstly we have to find the loss. In order to find the loss, we will apply the formula, $\text{Loss}=\dfrac{\text{Loss Percent}\times CP}{100}.$

Complete step-by-step solution:
We are given that Amina buys a book for Rs. 275, i.e. the mean cost price of the book is Rs. 275.
$C.P=275.......\left( i \right)$
She made a loss of 15 %.
$\text{Loss Percent}=15.......\left( ii \right)$
We know that,
$\text{Loss Percent}=\dfrac{\text{Loss }}{CP}\times 100$
From this, we get,
$\text{Loss}=\dfrac{\text{Loss Percent}\times CP}{100}.........\left( iii \right)$
Now, we will use the value of the CP and Loss Percent from (i) and (ii) respectively into (iii) to get the actual loss.
$\text{Loss}=\dfrac{\text{Loss Percent}\times CP}{100}$
Putting the values from (i) and (ii), we get,
$Loss=\dfrac{15\times 275}{100}$
$\Rightarrow Loss=\dfrac{4125}{100}$
$\Rightarrow Loss=41.25$
So, we get the loss taken by Amina as 41.25.
Now, we will find the selling price (S.P). We know that the selling price and loss are related as Loss = CP – SP.
From here, we get,
$SP=CP-Loss$
From earlier, we have CP = 275 and Loss = 41.25.
So putting these values, we get,
$SP=CP-Loss$
$\Rightarrow SP=275-41.25$
$\Rightarrow SP=233.75$
Therefore, Amina sells a book for Rs. 233.75.
Hence, option (b) is the right answer.

Note: We have to first convert loss % into the actual loss and then have to find the selling price. Students should not subtract loss % from cost price directly like SP = 275 – 15 = 260. This the wrong method.