A man buys some books for Rs 8000 and sells 1/4 of total at a loss of 20%. At what profit percent will he sell the remaining books so that the selling price and C.P. are equal?

Options

A. 0.08
B. 0.0666
C. 0.0333
D. 0.0633

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Determine the Cost Price (C.P.)
The total cost price of the books is given as Rs. 8000.

### Step 2: Calculate the Selling Price (S.P.) of 1/4 of the books
1/4 of the total cost price is:
\[ \text{C.P. of } \frac{1}{4} \text{ of books} = \frac{1}{4} \times 8000 = 2000 \text{ Rs.} \]

### Step 3: Calculate the Selling Price at a Loss of 20%
The selling price at a loss of 20% can be calculated using the formula:
\[ \text{S.P.} = \text{C.P.} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values:
\[ \text{S.P.} = 2000 \times \left(1 - \frac{20}{100}\right) = 2000 \times 0.8 = 1600 \text{ Rs.} \]

### Step 4: Calculate the Remaining Cost Price of the Books
The remaining cost price of the books is:
\[ \text{Remaining C.P.} = 8000 - 2000 = 6000 \text{ Rs.} \]

### Step 5: Calculate the Selling Price Required for No Profit No Loss
To achieve no profit or loss on the entire transaction, the total selling price must equal the total cost price:
\[ \text{Total C.P.} = 8000 \text{ Rs.} \]
The selling price of the remaining books must therefore be:
\[ \text{Required S.P.} = 8000 - 1600 = 6400 \text{ Rs.} \]

### Step 6: Calculate the Profit on the Remaining Books
The profit on the remaining books can be calculated as:
\[ \text{Profit} = \text{S.P.} - \text{C.P.} = 6400 - 6000 = 400 \text{ Rs.} \]

### Step 7: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit \%} = \left(\frac{\text{Profit}}{\text{C.P.}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \left(\frac{400}{6000}\right) \times 100 = \frac{40000}{6000} = \frac{20}{3} \approx 6.67\% \]

### Final Answer
The profit percentage at which he will sell the remaining books so that the selling price and cost price are equal is approximately **6.67%**.

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