There would be a 10% loss, if rice is sold at F 54 per kg. To earn a profit of 20%, the price of rice per kg will be

Options

A. Rs 72
B. Rs 65
C. Rs 63
D. Rs 70

Answer

To solve the problem step by step, we will first determine the cost price of the rice based on the information given about the selling price and the loss percentage. Then, we will calculate the selling price needed to achieve a desired profit percentage.

### Step 1: Determine the Cost Price
Given that there is a 10% loss when the rice is sold at Rs. 54 per kg, we can set up the following equation:

Let the cost price (CP) of the rice be Rs. 100x.

Since there is a 10% loss, the selling price (SP) can be expressed as:
\[ SP = CP - (10\% \text{ of } CP) \]
\[ SP = CP - 0.1 \times CP \]
\[ SP = 0.9 \times CP \]

Substituting the selling price:
\[ 54 = 0.9 \times (100x) \]

### Step 2: Solve for x
Now we can solve for x:
\[ 54 = 90x \]
\[ x = \frac{54}{90} \]
\[ x = \frac{3}{5} \]

### Step 3: Calculate the Cost Price
Now we can find the actual cost price:
\[ CP = 100x = 100 \times \frac{3}{5} = 60 \]

### Step 4: Calculate the Selling Price for 20% Profit
To find the selling price needed to achieve a 20% profit, we use the formula:
\[ SP = CP + (20\% \text{ of } CP) \]
\[ SP = CP + 0.2 \times CP \]
\[ SP = 1.2 \times CP \]

Substituting the cost price we found:
\[ SP = 1.2 \times 60 = 72 \]

### Conclusion
The price of rice per kg to earn a profit of 20% is Rs. 72.

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