A sells a box to B at a profit of 15%, sells the same to C for 1012 and makes a profit of 10% A's cost price is

Options

A. 720
B. 680
C. 880
D. 800

Answer

To solve the problem step by step, we will determine A's cost price based on the information provided about the selling prices and profit percentages.

### Step 1: Define Variables
Let A's cost price be \( x \).

### Step 2: Calculate Selling Price to B
A sells the box to B at a profit of 15%.
The selling price (SP) can be calculated using the formula:
\[ SP = CP + \text{Profit} = x + 0.15x = 1.15x \]
Thus, the selling price to B is:
\[ SP_B = 1.15x \]

### Step 3: Calculate Selling Price to C
A sells the same box to C for Rs. 1012 and makes a profit of 10%.
This means that the selling price to C can also be expressed as:
\[ SP_C = CP_B + \text{Profit} = CP_B + 0.10 \times CP_B = 1.10 \times CP_B \]
Since the cost price for B is the selling price for A, we can substitute \( CP_B \) with \( SP_B \):
\[ SP_C = 1.10 \times SP_B = 1.10 \times 1.15x = 1.265x \]

### Step 4: Set Up the Equation
We know that A sells the box to C for Rs. 1012, so we can set up the equation:
\[ 1.265x = 1012 \]

### Step 5: Solve for x
To find \( x \), we can rearrange the equation:
\[ x = \frac{1012}{1.265} \]

Now, calculate \( x \):
\[ x \approx 800 \]

### Conclusion
Thus, A's cost price is Rs. 800.

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