By selling 144 tin boxes, Ram suffers a loss equal to SP of 6 boxes. If the total CP of boxes is 7200, then what is the SP of a box ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
- Ram sells 144 tin boxes and suffers a loss equal to the selling price of 6 boxes.
- The total cost price (CP) of the 144 boxes is ₹7200.

### Step 2: Define the selling price (SP) of one box
Let the selling price of one box be \( x \). Therefore, the selling price of 144 boxes will be:
\[ \text{SP of 144 boxes} = 144 \times x = 144x \]

### Step 3: Calculate the loss
According to the problem, the loss incurred by Ram is equal to the selling price of 6 boxes:
\[ \text{Loss} = \text{SP of 6 boxes} = 6x \]

### Step 4: Relate CP, SP, and Loss
The relationship between Cost Price (CP), Selling Price (SP), and Loss can be expressed as:
\[ \text{CP} = \text{SP} + \text{Loss} \]
Substituting the values we have:
\[ 7200 = 144x + 6x \]

### Step 5: Simplify the equation
Combine like terms:
\[ 7200 = 150x \]

### Step 6: Solve for \( x \)
Now, to find \( x \), divide both sides by 150:
\[ x = \frac{7200}{150} \]
Calculating this gives:
\[ x = 48 \]

### Step 7: Conclusion
The selling price of one box is ₹48.

### Summary of Steps:
1. Define the selling price of one box as \( x \).
2. Calculate the selling price of 144 boxes as \( 144x \).
3. Determine the loss as \( 6x \).
4. Set up the equation relating CP, SP, and Loss.
5. Simplify and solve for \( x \).