The price of 12 kg of sugar is equal to that of 6 kg of rice. The price of 10 kg of sugar and 8 kg of rice Rs.1040. Find the price 1 kg of sugr
A.Rs.80
B.Rs. 70
C. Rs.60
D Rs. 40

Options

A. A
B. C
C. D
D. B

Answer

To solve the problem step by step, let's define the variables and equations based on the information given.

### Step 1: Define Variables
Let:
- \( S \) = price of 1 kg of sugar
- \( R \) = price of 1 kg of rice

### Step 2: Establish Relationships
From the problem, we know:
1. The price of 12 kg of sugar is equal to the price of 6 kg of rice:
\[ 12S = 6R \]
Simplifying this gives:
\[ 2S = R \quad \text{(Equation 1)} \]

2. The price of 10 kg of sugar and 8 kg of rice is Rs. 1040:
\[ 10S + 8R = 1040 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
Now, we can substitute \( R \) from Equation 1 into Equation 2:
\[ 10S + 8(2S) = 1040 \]
This simplifies to:
\[ 10S + 16S = 1040 \]
\[ 26S = 1040 \]

### Step 4: Solve for S
Now, divide both sides by 26 to find the price of 1 kg of sugar:
\[ S = \frac{1040}{26} \]
Calculating this gives:
\[ S = 40 \]

### Conclusion
The price of 1 kg of sugar is Rs. 40.

### Final Answer
D. Rs. 40