A trader allows a discount of 15% on a trolly bag having list price of Rs. 1360 and earns a profit of `15.6%`. What is the cost price (in Rs.) of the trolly bag?

Options

A. 1000
B. 1005
C. 1050
D. 1156

Answer

To find the cost price (CP) of the trolley bag, we can use the relationship between the cost price, marked price (MP), discount, and profit. Here are the steps to solve the problem:

### Step 1: Identify the given values
- List Price (MP) = Rs. 1360
- Discount = 15%
- Profit = 15.6%

### Step 2: Calculate the selling price (SP)
The selling price can be calculated using the formula:
\[ \text{SP} = \text{MP} - \text{Discount} \]
First, we need to calculate the discount amount:
\[ \text{Discount Amount} = \frac{15}{100} \times 1360 = 0.15 \times 1360 = 204 \]
Now, calculate the selling price:
\[ \text{SP} = 1360 - 204 = 1156 \]

### Step 3: Use the profit formula to find the cost price (CP)
The profit percentage is given as 15.6%. The relationship between SP, CP, and profit is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where profit can be expressed in terms of CP:
\[ \text{Profit} = \frac{15.6}{100} \times \text{CP} \]
Thus, we can rewrite the SP equation as:
\[ 1156 = \text{CP} + \frac{15.6}{100} \times \text{CP} \]
This can be simplified to:
\[ 1156 = \text{CP} \left(1 + \frac{15.6}{100}\right) \]
\[ 1156 = \text{CP} \left(\frac{100 + 15.6}{100}\right) \]
\[ 1156 = \text{CP} \left(\frac{115.6}{100}\right) \]

### Step 4: Solve for CP
To find CP, rearrange the equation:
\[ \text{CP} = \frac{1156 \times 100}{115.6} \]
Calculating the right side:
\[ \text{CP} = \frac{115600}{115.6} = 1000 \]

### Conclusion
The cost price (CP) of the trolley bag is Rs. 1000.

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