There would be `10%` loss if rice is sold at Rs `5.40%` per kg. At what price per kg should it be sold to earn a profit of `20%`

Options

A. Rs. `7.20`
B. Rs. `7.02`
C. Rs. `6.48`
D. Rs. 6

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the given information
We are given that selling rice at Rs 5.40 per kg results in a 10% loss. We need to find the selling price per kg that would yield a 20% profit.

### Step 2: Assume the Cost Price (CP)
Let's assume the Cost Price (CP) of the rice is Rs 100 per kg. This is a common approach to simplify calculations.

### Step 3: Calculate the Selling Price (SP) at 10% loss
If there is a 10% loss, the Selling Price (SP) can be calculated as follows:
\[ \text{SP} = \text{CP} - \text{Loss} \]
\[ \text{Loss} = 10\% \text{ of } CP = 10\% \text{ of } 100 = 10 \]
\[ \text{SP} = 100 - 10 = 90 \]

### Step 4: Relate the SP to the given price
We know that when the SP is Rs 90, it is equivalent to selling at Rs 5.40 per kg. Therefore, we can set up the equation:
\[ \text{SP} = 5.40 \text{ per kg} \]

### Step 5: Calculate the value of 1 kg
To find the value of 1 kg, we can use the relationship:
\[ \text{Value of 1 kg} = \frac{5.40}{90} \]
Calculating this gives:
\[ \text{Value of 1 kg} = 0.06 \]

### Step 6: Calculate the SP for 20% profit
Now, we need to find the SP that would give us a 20% profit. The profit can be calculated as:
\[ \text{Profit} = 20\% \text{ of } CP = 20\% \text{ of } 100 = 20 \]
Thus, the new SP will be:
\[ \text{SP} = \text{CP} + \text{Profit} = 100 + 20 = 120 \]

### Step 7: Calculate the new selling price
Now we can find the selling price for 20% profit using the value of 1 kg:
\[ \text{New SP} = \text{Value of 1 kg} \times 120 \]
Substituting the value we calculated:
\[ \text{New SP} = 0.06 \times 120 \]
Calculating this gives:
\[ \text{New SP} = 7.20 \]

### Conclusion
The price at which the rice should be sold to earn a profit of 20% is Rs 7.20 per kg.

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