A book is sold at profit of Rs. 20, which is 10% of its cost price. If its C.P. is increased by 50% and it is still sold at a profit of 10%, then find the new profit.

Options

A. Rs. 30
B. Rs. 50
C. Rs. 60
D. Rs. 300

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (C.P.)
We know that the profit of Rs. 20 is 10% of the cost price. Let the cost price be denoted as \( CP \).

Given:
\[ \text{Profit} = 10\% \text{ of } CP \]
\[ 20 = 0.10 \times CP \]

To find \( CP \), we can rearrange the equation:
\[ CP = \frac{20}{0.10} = 200 \]

### Step 2: Calculate the New Cost Price after 50% Increase
The cost price is increased by 50%. We need to calculate the new cost price.

\[ \text{Increase} = 50\% \text{ of } 200 = 0.50 \times 200 = 100 \]

Now, add this increase to the original cost price:
\[ \text{New C.P.} = 200 + 100 = 300 \]

### Step 3: Calculate the Selling Price at 10% Profit on the New Cost Price
Now, we need to find the selling price when the new cost price is sold at a profit of 10%.

\[ \text{Selling Price} = \text{New C.P.} + \text{Profit} \]
\[ \text{Profit} = 10\% \text{ of } 300 = 0.10 \times 300 = 30 \]

Thus, the selling price is:
\[ \text{Selling Price} = 300 + 30 = 330 \]

### Step 4: Determine the New Profit
The new profit is the profit made from selling the book at the new selling price.

\[ \text{New Profit} = \text{Selling Price} - \text{New C.P.} \]
\[ \text{New Profit} = 330 - 300 = 30 \]

### Final Answer
The new profit is Rs. 30.

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