The cost of 3 oranges and 12 apples is Rs. 9.60 and the cost of 5 oranges and 7 apples is Rs. 6.90. Find the cost of apples per dozen.

Answer

To solve the problem, we need to set up a system of linear equations based on the information given. Let's denote the cost of one orange as \( x \) (in Rs.) and the cost of one apple as \( y \) (in Rs.).

### Step 1: Set up the equations

From the problem, we have two pieces of information:

1. The cost of 3 oranges and 12 apples is Rs. 9.60.
\[ 3x + 12y = 9.60 \]

2. The cost of 5 oranges and 7 apples is Rs. 6.90.
\[ 5x + 7y = 6.90 \]

### Step 2: Simplify the first equation

We can simplify the first equation by dividing all terms by 3:
\[ x + 4y = 3.20 \quad \text{(Equation 1)} \]

### Step 3: Keep the second equation as it is

The second equation remains:
\[ 5x + 7y = 6.90 \quad \text{(Equation 2)} \]

### Step 4: Eliminate \( x \)

To eliminate \( x \), we can multiply Equation 1 by 5:
\[ 5(x + 4y) = 5(3.20) \]
This simplifies to:
\[ 5x + 20y = 16.00 \quad \text{(Equation 3)} \]

### Step 5: Subtract Equation 2 from Equation 3

Now, we will subtract Equation 2 from Equation 3:
\[ (5x + 20y) - (5x + 7y) = 16.00 - 6.90 \]
This simplifies to:
\[ 20y - 7y = 16.00 - 6.90 \]
\[ 13y = 9.10 \]

### Step 6: Solve for \( y \)

Now, we can solve for \( y \):
\[ y = \frac{9.10}{13} = 0.70 \]

### Step 7: Find the cost of apples per dozen

Since \( y \) represents the cost of one apple, the cost of 12 apples (which is a dozen) will be:
\[ 12y = 12 \times 0.70 = 8.40 \]

### Final Answer

The cost of apples per dozen is Rs. 8.40.

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