By selling a commodity for Rs. 72,000, a person made a profit of 20%. What was the cost price of that commodity ?

Question

Accepted Answer

To determine the cost price of the commodity, we need to understand the relationship between cost price, selling price, and profit percentage. The formula to calculate the selling price (SP) when the cost price (CP) and profit percentage are known is:

$$ \text{SP} = \text{CP} + \left(\frac{\text{Profit Percentage}}{100} \times \text{CP}\right) $$

Given:
- Selling Price (SP) = Rs. 72,000
- Profit Percentage = 20%

We can rearrange the formula to find the cost price (CP):

$$ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) $$

Substituting the given values:

$$ 72,000 = \text{CP} \times \left(1 + \frac{20}{100}\right) $$
$$ 72,000 = \text{CP} \times 1.2 $$

To find the cost price (CP), divide the selling price by 1.2:

$$ \text{CP} = \frac{72,000}{1.2} $$
$$ \text{CP} = 60,000 $$

Thus, the cost price of the commodity is Rs. 60,000, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (Rs. 50,000):** If the cost price were Rs. 50,000, the selling price with a 20% profit would be:
  $$ \text{SP} = 50,000 \times 1.2 = 60,000 $$
  This does not match the given selling price of Rs. 72,000, so Option 2 is incorrect.

- **Option 3 (Rs. 40,000):** If the cost price were Rs. 40,000, the selling price with a 20% profit would be:
  $$ \text{SP} = 40,000 \times 1.2 = 48,000 $$
  This does not match the given selling price of Rs. 72,000, so Option 3 is incorrect.

- **Option 4 (Rs. 65,000):** If the cost price were Rs. 65,000, the selling price with a 20% profit would be:
  $$ \text{SP} = 65,000 \times 1.2 = 78,000 $$
  This does not match the given selling price of Rs. 72,000, so Option 4 is incorrect.

Therefore, the correct answer is Option 1, Rs. 60,000.