A shopkeeper sold a bat at the profit of 20%, if he sold it at Rs 17.5 more then he would have earned 30% profit. Find at what price shopkeeper should sell the hat to earn profit of 60%?

Options

A. 280Rs
B. 260Rs
C. 240Rs
D. 220Rs

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
- The shopkeeper sold a bat at a profit of 20%.
- If he sold it for Rs 17.5 more, he would have earned a profit of 30%.

### Step 2: Define variables
Let the Cost Price (CP) of the bat be \( CP \).

### Step 3: Calculate Selling Prices (SP)
1. Selling Price at 20% profit:
\[ SP_1 = CP + 20\% \text{ of } CP = CP + 0.2 \times CP = 1.2 \times CP \]

2. Selling Price at 30% profit:
\[ SP_2 = CP + 30\% \text{ of } CP = CP + 0.3 \times CP = 1.3 \times CP \]

### Step 4: Set up the equation based on the information given
According to the problem, the difference between the two selling prices is Rs 17.5:
\[ SP_2 - SP_1 = 17.5 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ (1.3 \times CP) - (1.2 \times CP) = 17.5 \]
This simplifies to:
\[ 0.1 \times CP = 17.5 \]

### Step 5: Solve for the Cost Price (CP)
To find \( CP \):
\[ CP = \frac{17.5}{0.1} = 175 \]

### Step 6: Calculate the Selling Price for 60% profit
Now, we need to find the selling price when the profit is 60%:
\[ SP_3 = CP + 60\% \text{ of } CP = CP + 0.6 \times CP = 1.6 \times CP \]
Substituting the value of \( CP \):
\[ SP_3 = 1.6 \times 175 \]

### Step 7: Perform the multiplication
Calculating \( SP_3 \):
\[ SP_3 = 280 \]

### Conclusion
The shopkeeper should sell the bat for Rs 280 to earn a profit of 60%.