A sold a thing to B with 5% loss and B sold it to C at 10% loss. If the cost price for C is Rs 855 then find out the cost price of A.

Options

A. Rs 10000
B. Rs 1000
C. Rs 1050
D. Rs 100

Answer

To solve the problem, we need to find the cost price of A based on the given information about the transactions between A, B, and C.

### Step-by-step Solution:

1. **Understanding the Losses**:
- A sold the item to B at a 5% loss.
- B sold the item to C at a 10% loss.
- The cost price for C is given as Rs 855.

2. **Finding the Selling Price of B**:
- Let the cost price of A be \( CP_A \).
- Since A sold the item to B at a 5% loss, the selling price for B can be calculated as:
\[ SP_B = CP_A - (5\% \text{ of } CP_A) = CP_A - 0.05 \times CP_A = 0.95 \times CP_A \]

3. **Finding the Selling Price of C**:
- B sold the item to C at a 10% loss. Therefore, the selling price for C can be calculated as:
\[ SP_C = SP_B - (10\% \text{ of } SP_B) = SP_B - 0.10 \times SP_B = 0.90 \times SP_B \]
- Substituting \( SP_B \) from the previous step:
\[ SP_C = 0.90 \times (0.95 \times CP_A) = 0.855 \times CP_A \]

4. **Setting Up the Equation**:
- We know that the selling price for C is Rs 855:
\[ 0.855 \times CP_A = 855 \]

5. **Calculating the Cost Price of A**:
- To find \( CP_A \), we can rearrange the equation:
\[ CP_A = \frac{855}{0.855} \]
- Performing the division:
\[ CP_A = 1000 \]

### Final Answer:
The cost price of A is Rs 1000.