The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is Rs.

Options

A. 660
B. 620
C. 820
D. 780

Answer

To solve the problem step by step, we will first define the variables and then set up equations based on the information given.

### Step 1: Define the Variables
Let:
- A = Price of one apple
- B = Price of one orange

### Step 2: Set Up the First Equation
According to the problem, the price of 80 apples is equal to the price of 120 oranges. This gives us our first equation:
\[ 80A = 120B \]
Dividing both sides by 40, we simplify this to:
\[ 2A = 3B \]
Rearranging gives us:
\[ B = \frac{2A}{3} \]
(Equation 1)

### Step 3: Set Up the Second Equation
The problem states that the price of 60 apples and 75 oranges together is Rs. 1320. This gives us our second equation:
\[ 60A + 75B = 1320 \]
We can simplify this equation by dividing everything by 15:
\[ 4A + 5B = 88 \]
(Equation 2)

### Step 4: Substitute Equation 1 into Equation 2
Now we substitute the value of B from Equation 1 into Equation 2:
\[ 4A + 5\left(\frac{2A}{3}\right) = 88 \]
This simplifies to:
\[ 4A + \frac{10A}{3} = 88 \]
To eliminate the fraction, multiply the entire equation by 3:
\[ 12A + 10A = 264 \]
Combining like terms gives:
\[ 22A = 264 \]
Dividing both sides by 22:
\[ A = 12 \]

### Step 5: Find the Value of B
Now that we have the value of A, we can find B using Equation 1:
\[ B = \frac{2A}{3} = \frac{2 \times 12}{3} = 8 \]

### Step 6: Calculate the Total Price of 25 Apples and 40 Oranges
Now we need to find the total price of 25 apples and 40 oranges:
\[ \text{Total Price} = 25A + 40B \]
Substituting the values of A and B:
\[ = 25 \times 12 + 40 \times 8 \]
Calculating each part:
\[ = 300 + 320 = 620 \]

### Final Answer
The total price of 25 apples and 40 oranges is Rs. 620.

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