If the rice is sold at Rs 48 per kg, then there would be a 20% loss. To earn a profit of 20% what should be the price of rice (per kg)?

Options

A. 72
B. 76
C. 78
D. 84

Answer

To solve the problem, we need to determine the cost price (CP) of the rice first, based on the information given about the selling price (SP) and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)

Given that the selling price (SP) is Rs 48 per kg and there is a loss of 20%, we can use the formula for loss:

\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]

Since there is a 20% loss, we can express this in terms of the cost price:

\[ \text{Selling Price} = \text{Cost Price} - 20\% \text{ of Cost Price} \]

This can be rewritten as:

\[ \text{Selling Price} = \text{Cost Price} \times (1 - 0.20) = \text{Cost Price} \times 0.80 \]

Now, substituting the selling price into the equation:

\[ 48 = CP \times 0.80 \]

To find the cost price (CP), we rearrange the equation:

\[ CP = \frac{48}{0.80} \]

Calculating this gives:

\[ CP = 60 \]

### Step 2: Determine the Selling Price for a 20% Profit

Now that we have the cost price, we can find the selling price required to achieve a profit of 20%. The formula for profit is:

\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]

Where profit can be expressed as:

\[ \text{Profit} = 20\% \text{ of Cost Price} = 0.20 \times CP \]

Substituting the cost price we found:

\[ \text{Profit} = 0.20 \times 60 = 12 \]

Now, substituting back into the selling price formula:

\[ \text{Selling Price} = CP + \text{Profit} = 60 + 12 = 72 \]

### Final Answer

The price of rice per kg to earn a profit of 20% should be **Rs 72**.

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