The cost of the Red, Green and Blue colours per kg is Rs. 20, Rs. 15 and Rs. 18 respectively. Rang Mahal is a renowned building in which these three colours are being used in the ratio of 3 : 2 : 4. The average cost of all the three colours used per kg is :

Options

A. 18
B. 20
C. 17.66
D. can't be determined

Answer

To find the average cost of the Red, Green, and Blue colors used in Rang Mahal, we follow these steps:

### Step 1: Determine the ratio of colors
The colors are used in the ratio of Red:Green:Blue = 3:2:4.

### Step 2: Assign weights based on the ratio
Let the weights of the colors be:
- Red = 3 parts
- Green = 2 parts
- Blue = 4 parts

### Step 3: Calculate the total parts
Total parts = 3 (Red) + 2 (Green) + 4 (Blue) = 9 parts.

### Step 4: Find the cost per kg for each color
- Cost of Red = Rs. 20/kg
- Cost of Green = Rs. 15/kg
- Cost of Blue = Rs. 18/kg

### Step 5: Calculate the total cost for each color based on the ratio
- Total cost of Red = 3 parts × Rs. 20/kg = Rs. 60
- Total cost of Green = 2 parts × Rs. 15/kg = Rs. 30
- Total cost of Blue = 4 parts × Rs. 18/kg = Rs. 72

### Step 6: Calculate the total cost of all colors
Total cost = Total cost of Red + Total cost of Green + Total cost of Blue
Total cost = Rs. 60 + Rs. 30 + Rs. 72 = Rs. 162

### Step 7: Calculate the average cost per kg
Average cost = Total cost / Total parts
Average cost = Rs. 162 / 9 parts = Rs. 18

### Final Answer
The average cost of all the three colors used per kg is Rs. 18.

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