The cost of 15 kg of groundnuts and 4kg of cashews is Rs. 7,000 . The cost of 10 kg of cashews is equal to 25 kg of groundnuts. Find the cost of groundnut per kg.
A. Rs, 320
B. Rs, 700
C. Rs, 540
D. Rs, 280

Options

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

Answer

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let the cost of groundnuts per kg be \( x \) and the cost of cashews per kg be \( y \).

### Step 2: Set Up the First Equation
From the information given, we know that the cost of 15 kg of groundnuts and 4 kg of cashews is Rs. 7000. This can be expressed as:
\[ 15x + 4y = 7000 \]
This is our **Equation 1**.

### Step 3: Set Up the Second Equation
We are also told that the cost of 10 kg of cashews is equal to the cost of 25 kg of groundnuts. This can be expressed as:
\[ 10y = 25x \]
We can simplify this equation by dividing both sides by 5:
\[ 2y = 5x \]
This is our **Equation 2**.

### Step 4: Express y in Terms of x
From Equation 2, we can express \( y \) in terms of \( x \):
\[ y = \frac{5}{2}x \]

### Step 5: Substitute y in Equation 1
Now we will substitute \( y \) in Equation 1:
\[ 15x + 4\left(\frac{5}{2}x\right) = 7000 \]
This simplifies to:
\[ 15x + 10x = 7000 \]
\[ 25x = 7000 \]

### Step 6: Solve for x
Now, we can solve for \( x \):
\[ x = \frac{7000}{25} \]
\[ x = 280 \]

### Step 7: Conclusion
The cost of groundnuts per kg is Rs. 280.

### Final Answer
Thus, the correct option is **D. Rs. 280**.

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