A person sold a book at 20% profit. If he had bought it at 10% less cost and sold for Rs 90 more then he would have gained 40% profit. Find cost price of book.

Options

A. A)Rs 800
B. B)Rs 1600
C. C)Rs 1500
D. D)None of these

Answer

To solve the problem step by step, we will denote the cost price of the book as \( CP \).

### Step 1: Define the Cost Price
Let the cost price of the book be \( CP = 100K \), where \( K \) is a constant.

### Step 2: Calculate Selling Price at 20% Profit
If the book is sold at a 20% profit, the selling price \( SP_1 \) can be calculated as follows:
\[ SP_1 = CP + 20\% \text{ of } CP = 100K + 0.2 \times 100K = 120K \]

### Step 3: Calculate New Cost Price
If the person had bought the book at 10% less cost, the new cost price \( CP' \) would be:
\[ CP' = CP - 10\% \text{ of } CP = 100K - 0.1 \times 100K = 90K \]

### Step 4: Calculate Selling Price for 40% Profit
If he sold the book for Rs 90 more than the previous selling price and gained a 40% profit, the new selling price \( SP_2 \) can be calculated as:
\[ SP_2 = CP' + 40\% \text{ of } CP' = 90K + 0.4 \times 90K = 90K + 36K = 126K \]

### Step 5: Set Up the Equation
According to the problem, the new selling price is also Rs 90 more than the previous selling price:
\[ SP_2 = SP_1 + 90 \]
Substituting the values we have:
\[ 126K = 120K + 90 \]

### Step 6: Solve for K
Now, we can solve for \( K \):
\[ 126K - 120K = 90 \]
\[ 6K = 90 \]
\[ K = \frac{90}{6} = 15 \]

### Step 7: Calculate the Original Cost Price
Now that we have the value of \( K \), we can find the original cost price \( CP \):
\[ CP = 100K = 100 \times 15 = 1500 \]

### Final Answer
The cost price of the book is Rs 1500.

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