The profit earned by a shopkeeper by selling a bucket at a gain of 8% is 28 more than when he sells it at a loss of 8%. The cost price (in Rupees) of the bucket is

Options

A. 170
B. 190
C. 175
D. 165

Answer

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

### Step 1: Define the Variables
Let the cost price (CP) of the bucket be \( x \) Rupees.

### Step 2: Calculate Selling Price at 8% Profit
When the shopkeeper sells the bucket at an 8% profit, the selling price (SP) can be calculated as:
\[ SP_{profit} = CP + (8\% \text{ of } CP) = x + 0.08x = 1.08x \]

### Step 3: Calculate Selling Price at 8% Loss
When the shopkeeper sells the bucket at an 8% loss, the selling price (SP) can be calculated as:
\[ SP_{loss} = CP - (8\% \text{ of } CP) = x - 0.08x = 0.92x \]

### Step 4: Set Up the Equation
According to the problem, the profit earned by selling at an 8% profit is 28 Rupees more than the loss incurred by selling at an 8% loss. Therefore, we can write the equation:
\[ SP_{profit} - SP_{loss} = 28 \]
Substituting the expressions for SP:
\[ 1.08x - 0.92x = 28 \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ (1.08x - 0.92x) = 0.16x \]
Thus, the equation becomes:
\[ 0.16x = 28 \]

### Step 6: Solve for x
To find the cost price \( x \), divide both sides by 0.16:
\[ x = \frac{28}{0.16} \]
Calculating the right side:
\[ x = 175 \]

### Conclusion
The cost price of the bucket is \( \text{Rs. } 175 \).