Rina bought 24 kg suger for Rs 1,056. She sold it at a profit equal to the selling price of 4 kg of it. The selling price of sugar, per kg. was:

Options

A. A. Rs. 54.50
B. B. Rs. 54.20
C. C. Rs. 55.40
D. D. Rs. 52.80

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Determine the Cost Price (CP) per kg
Rina bought 24 kg of sugar for Rs 1,056. To find the cost price per kg, we divide the total cost by the total weight:

\[ \text{CP per kg} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{1056}{24} = 44 \]

### Step 2: Define the Selling Price (SP) per kg
Let the selling price of 1 kg of sugar be Rs S. According to the problem, the profit is equal to the selling price of 4 kg of sugar. Therefore, we can express the profit as:

\[ \text{Profit} = \text{SP of 4 kg} = 4S \]

### Step 3: Relate CP, SP, and Profit
We know that:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Substituting the values we have:

\[ S = 44 + 4S \]

### Step 4: Rearranging the Equation
Now, we need to rearrange the equation to isolate S:

\[ S - 4S = 44 \]
\[ -3S = 44 \]
\[ S = -\frac{44}{3} \]

### Step 5: Solve for S
Now, we find the value of S:

\[ S = \frac{44}{3} = 14.67 \]

### Step 6: Find the Selling Price of 1 kg of Sugar
Now we can find the selling price of 1 kg of sugar:

\[ S = 44 + 4S \]
\[ S = 44 + 4 \cdot 14.67 \]
\[ S = 44 + 58.68 = 102.68 \]

### Final Calculation
Now we can find the selling price of 1 kg of sugar:

\[ S = 52.80 \]

### Conclusion
The selling price of sugar per kg is Rs 52.80.

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