Ram bought 5 dozen mangoes ,8 dozen bananas and 4 dozen oranges , the cost price of mango banana and orange are Rs. 40, Rs, 25 and Rs. 20 per dozen ,Represent the fruits in row matrix and price of the fruits .

Explanation

To solve the problem step by step, we will represent the quantities of fruits and their respective prices in matrix form and then calculate the total cost.

### Step 1: Represent the quantities of fruits in a row matrix
We have:
- 5 dozen mangoes
- 8 dozen bananas
- 4 dozen oranges

We can represent this information in a row matrix \( F \):
\[ F = \begin{bmatrix} 5 & 8 & 4 \end{bmatrix} \]

### Step 2: Represent the prices of the fruits in a column matrix
The prices per dozen are:
- Mangoes: Rs. 40
- Bananas: Rs. 25
- Oranges: Rs. 20

We can represent this information in a column matrix \( P \):
\[ P = \begin{bmatrix} 40 \\ 25 \\ 20 \end{bmatrix} \]

### Step 3: Calculate the total cost
To find the total cost, we will multiply the row matrix \( F \) by the column matrix \( P \):
\[ \text{Total Cost} = F \cdot P = \begin{bmatrix} 5 & 8 & 4 \end{bmatrix} \cdot \begin{bmatrix} 40 \\ 25 \\ 20 \end{bmatrix} \]

### Step 4: Perform the matrix multiplication
The multiplication will be done as follows:
\[ \text{Total Cost} = (5 \times 40) + (8 \times 25) + (4 \times 20) \]
Calculating each term:
- \( 5 \times 40 = 200 \)
- \( 8 \times 25 = 200 \)
- \( 4 \times 20 = 80 \)

Now, adding these values together:
\[ \text{Total Cost} = 200 + 200 + 80 = 480 \]

### Final Answer
The total cost of the fruits is Rs. 480.

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