P sells a table to Q at a profit of 10% and Q sells it to R at a profit of 12%. If R pays Rs 246.40 for it, then how much had P paid for it ?

Options

A. 300
B. 248
C. 346
D. 200

Answer

To find out how much P paid for the table, we need to work backwards from the final selling price that R paid. Here’s the step-by-step solution:

### Step 1: Determine the Selling Price for Q
R pays Rs. 246.40 for the table. Since Q sells the table to R at a profit of 12%, we can find the cost price for Q (CP_Q) using the formula for selling price (SP) with profit:

\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]

Here, SP for R is Rs. 246.40, and the profit percentage for Q is 12%. Therefore:

\[ 246.40 = CP_Q \times \left(1 + \frac{12}{100}\right) \]

This simplifies to:

\[ 246.40 = CP_Q \times 1.12 \]

### Step 2: Calculate CP_Q
To find CP_Q, we rearrange the equation:

\[ CP_Q = \frac{246.40}{1.12} \]

Calculating this gives:

\[ CP_Q = 220 \]

### Step 3: Determine the Selling Price for P
Now that we have the cost price for Q (Rs. 220), we can find out how much P sold it for. P sells the table to Q at a profit of 10%. We use the same formula for selling price:

\[ SP = CP_P \times \left(1 + \frac{Profit\%}{100}\right) \]

Here, SP for Q is Rs. 220, and the profit percentage for P is 10%. Therefore:

\[ 220 = CP_P \times \left(1 + \frac{10}{100}\right) \]

This simplifies to:

\[ 220 = CP_P \times 1.10 \]

### Step 4: Calculate CP_P
To find CP_P, we rearrange the equation:

\[ CP_P = \frac{220}{1.10} \]

Calculating this gives:

\[ CP_P = 200 \]

### Conclusion
Thus, P paid Rs. 200 for the table.

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