# 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

Answer

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334.8k+ 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,

\[SP=CP-Loss\]

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.

Last updated date: 26th Sep 2023

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