The selling price of a toy was Rs. 540. If the profit made by shopkeeper was 20%, what was the cost price of this toy?

Question

Accepted Answer

To determine the cost price of the toy, we need to understand the relationship between the selling price, cost price, and profit percentage. The selling price (SP) of the toy is given as Rs. 540, and the profit percentage is 20%.

The formula to calculate the cost price (CP) when the selling price and profit percentage are known is:

$$ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit Percentage}}{100}} $$

Substituting the given values into the formula:

$$ \text{CP} = \frac{540}{1 + \frac{20}{100}} $$

$$ \text{CP} = \frac{540}{1 + 0.2} $$

$$ \text{CP} = \frac{540}{1.2} $$

$$ \text{CP} = 450 $$

Therefore, the cost price of the toy is Rs. 450, which corresponds to Option 4.

**Explanation for why each of the other options is incorrect:**

1. **Option 1: Rs. 385** - If the cost price were Rs. 385, the profit would be calculated as follows:
   $$ \text{Profit} = \text{SP} - \text{CP} = 540 - 385 = 155 $$
   The profit percentage would then be:
   $$ \text{Profit Percentage} = \left(\frac{155}{385}\right) \times 100 \approx 40.26\% $$
   This is not equal to the given profit percentage of 20%.

2. **Option 2: Rs. 375** - If the cost price were Rs. 375, the profit would be:
   $$ \text{Profit} = 540 - 375 = 165 $$
   The profit percentage would be:
   $$ \text{Profit Percentage} = \left(\frac{165}{375}\right) \times 100 \approx 44\% $$
   This is not equal to the given profit percentage of 20%.

3. **Option 3: Rs. 350** - If the cost price were Rs. 350, the profit would be:
   $$ \text{Profit} = 540 - 350 = 190 $$
   The profit percentage would be:
   $$ \text{Profit Percentage} = \left(\frac{190}{350}\right) \times 100 \approx 54.29\% $$
   This is not equal to the given profit percentage of 20%.

In conclusion, only Option 4 (Rs. 450) satisfies the condition of a 20% profit on the selling price of Rs. 540, making it the correct answer.