A certain product C is made of two ingredients A and B in the proportion of 2: 5. The price of A is three times that of B. The overall cost of C is ₹5.20 per kg including labour charges of 80 paisa per kg. Find the cost of B per kg ?

Options

A. ₹8.40
B. ₹4.20
C. ₹4.80
D. ₹2.80

Explanation

To solve the problem step by step, we will first define the variables and then use the information given in the question to find the cost of ingredient B per kg.

### Step 1: Define the variables
Let the cost of ingredient B be ₹x per kg.
Then, the cost of ingredient A, which is three times that of B, will be ₹3x per kg.

### Step 2: Determine the total cost of ingredients A and B in the mixture
The product C is made of ingredients A and B in the ratio of 2:5.
This means that for every 2 parts of A, there are 5 parts of B.
The total parts = 2 + 5 = 7 parts.

The cost of A in the mixture:
- Since A is in 2 parts, the cost of A in the mixture = (2/7) * (3x) = (6x/7) per kg.

The cost of B in the mixture:
- Since B is in 5 parts, the cost of B in the mixture = (5/7) * x = (5x/7) per kg.

### Step 3: Calculate the total cost of the mixture (ingredients A and B)
The total cost of the mixture (A + B) will be:
Total cost = Cost of A + Cost of B
Total cost = (6x/7) + (5x/7) = (11x/7) per kg.

### Step 4: Include the labor charges
According to the problem, the overall cost of product C is ₹5.20 per kg, which includes labor charges of ₹0.80 per kg.
Thus, the cost of the ingredients alone (A + B) can be calculated as:
Cost of ingredients = Total cost of C - Labor charges
Cost of ingredients = ₹5.20 - ₹0.80 = ₹4.40 per kg.

### Step 5: Set up the equation
Now we can set up the equation based on the cost of ingredients:
(11x/7) = ₹4.40.

### Step 6: Solve for x
To find x, multiply both sides by 7:
11x = 4.40 * 7
11x = ₹30.80.

Now, divide by 11:
x = ₹30.80 / 11
x = ₹2.80.

### Step 7: Conclusion
The cost of ingredient B per kg is ₹2.80.