The SP of 36 kg rice is Rs. 1080. If profit is equal to SP of 10 kg, then find the Cost price of 6 kg rice.

Options

A. Rs. 150
B. Rs. 180
C. Rs. 130
D. Rs. 160

Answer

To solve the problem, we need to find the cost price of 6 kg of rice given the selling price (SP) and the profit condition. Let's break it down step by step.

### Step 1: Determine the Selling Price (SP) of 1 kg of rice
The selling price of 36 kg of rice is given as Rs. 1080.

To find the selling price per kg:
\[ \text{SP of 1 kg} = \frac{\text{SP of 36 kg}}{36} = \frac{1080}{36} = 30 \text{ Rs/kg} \]

### Step 2: Calculate the Profit
According to the problem, the profit is equal to the selling price of 10 kg of rice.

First, we calculate the SP of 10 kg of rice:
\[ \text{SP of 10 kg} = 10 \times \text{SP of 1 kg} = 10 \times 30 = 300 \text{ Rs} \]

So, the profit is Rs. 300.

### Step 3: Relate Selling Price, Cost Price, and Profit
We know that:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Where CP is the cost price.

From the previous steps, we can express this as:
\[ 300 = 1080 - \text{CP of 36 kg} \]

### Step 4: Calculate the Cost Price (CP) of 36 kg of rice
Rearranging the equation gives us:
\[ \text{CP of 36 kg} = 1080 - 300 = 780 \text{ Rs} \]

### Step 5: Find the Cost Price (CP) of 1 kg of rice
Now, we can find the cost price per kg:
\[ \text{CP of 1 kg} = \frac{\text{CP of 36 kg}}{36} = \frac{780}{36} = 21.67 \text{ Rs/kg} \text{ (approximately)} \]

### Step 6: Calculate the Cost Price (CP) of 6 kg of rice
Finally, to find the cost price of 6 kg of rice:
\[ \text{CP of 6 kg} = 6 \times \text{CP of 1 kg} = 6 \times 21.67 \approx 130 \text{ Rs} \]

### Conclusion
The cost price of 6 kg of rice is approximately Rs. 130.

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