M sold a printer to N at a profit of `10%` and N sold it to P at profit of `4%` paid Rs. 14,300 what was the cost price to M ?

Options

A. Rs. 12,500
B. Rs. 12,355
C. Rs. 12,300
D. Rs. 12,480

Answer

To find the cost price of the printer to M, we will work through the problem step by step.

### Step 1: Understand the Selling Prices and Profits
- M sells the printer to N at a profit of 10%.
- N sells the printer to P at a profit of 4%.
- The final selling price to P is Rs. 14,300.

### Step 2: Set Up the Selling Price Equations
Let’s denote:
- CP_M = Cost Price to M
- SP_N = Selling Price to N
- SP_P = Selling Price to P (which is given as Rs. 14,300)

From the information given:
1. M sells to N at a profit of 10%:
\[ SP_N = CP_M + 10\% \text{ of } CP_M = CP_M + 0.10 \times CP_M = 1.10 \times CP_M \]

2. N sells to P at a profit of 4%:
\[ SP_P = SP_N + 4\% \text{ of } SP_N = SP_N + 0.04 \times SP_N = 1.04 \times SP_N \]

### Step 3: Substitute SP_N into SP_P Equation
Now we can express SP_P in terms of CP_M:
\[ SP_P = 1.04 \times SP_N = 1.04 \times (1.10 \times CP_M) = 1.144 \times CP_M \]

### Step 4: Set Up the Equation with the Given Selling Price
We know that SP_P = Rs. 14,300, so we can set up the equation:
\[ 1.144 \times CP_M = 14,300 \]

### Step 5: Solve for CP_M
To find CP_M, we divide both sides by 1.144:
\[ CP_M = \frac{14,300}{1.144} \]

### Step 6: Calculate the Value
Now we perform the division:
\[ CP_M = 12,500 \]

### Conclusion
The cost price to M was Rs. 12,500.