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

129k+ views
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,
From earlier, we have CP = 275 and Loss = 41.25.
So putting these values, we get,
\[\Rightarrow SP=275-41.25\]
\[\Rightarrow SP=233.75\]
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.