A wholesaler sells a watch to a retaller at a profit of 33% and the retailer sells it to a customer at a loss of 20%. If the customer pays Rs. 2,181.2, what had it cost the wholesaler?

Options

A. Rs.2050
B. Rs.2320
C. Rs.2712
D. Rs.1780

Answer

To solve the problem step by step, we need to determine how much the wholesaler originally paid for the watch, given the selling price to the customer and the profit and loss percentages involved.

### Step 1: Understand the Selling Price to the Customer
The customer pays Rs. 2,181.2 for the watch.

**Hint:** Identify the final selling price after all profit and loss adjustments.

### Step 2: Calculate the Retailer's Selling Price
The retailer sells the watch at a loss of 20%. This means the selling price (SP) for the retailer can be calculated using the formula for loss:
\[ \text{SP} = \text{Cost Price} \times (1 - \text{Loss Percentage}) \]
Let the cost price for the retailer be \( Y \). Since the retailer sells at a loss of 20%, we have:
\[ 2,181.2 = Y \times (1 - 0.20) \]
\[ 2,181.2 = Y \times 0.80 \]

**Hint:** Rearranging the equation will help you find the cost price for the retailer.

### Step 3: Solve for the Retailer's Cost Price
To find \( Y \):
\[ Y = \frac{2,181.2}{0.80} \]
\[ Y = 2,726.5 \]

**Hint:** Use division to isolate \( Y \).

### Step 4: Calculate the Wholesaler's Selling Price
The retailer bought the watch from the wholesaler at a profit of 33%. Thus, the cost price for the wholesaler (let's denote it as \( X \)) can be calculated using the formula for profit:
\[ Y = X \times (1 + \text{Profit Percentage}) \]
Substituting the values:
\[ 2,726.5 = X \times (1 + 0.33) \]
\[ 2,726.5 = X \times 1.33 \]

**Hint:** Again, rearranging the equation will help you find the cost price for the wholesaler.

### Step 5: Solve for the Wholesaler's Cost Price
To find \( X \):
\[ X = \frac{2,726.5}{1.33} \]
Calculating this gives:
\[ X \approx 2,050 \]

**Hint:** Perform the division to find the wholesaler's cost price.

### Conclusion
The cost to the wholesaler for the watch was Rs. 2,050.