Answer :
To find the price of the third variety of rice per kg, we need to use the concept of weighted averages based on the given ratio of mixing.
Let's break it down step by step:
Identify the information given in the problem:
- Price of the first type of rice: ₹43/kg
- Price of the second type of rice: ₹67/kg
- Price of the mixture: ₹96/kg
- Ratio of mixing: 2:1:5
Understand how the ratio divides the quantities used in mixing:
The ratio 2:1:5 means that for every 2 parts of the first rice, there is 1 part of the second rice, and 5 parts of the third variety.
Assume the quantities mixed according to the ratio:
- Let the total quantity be 8x (the sum of the parts of the ratio 2+1+5).
- Therefore, the quantity of the first type of rice = 2x
- The quantity of the second type of rice = 1x
- The quantity of the third type of rice = 5x
Set up the equation using the concept of weighted average:
Since the overall price of the mixture is given, we can write the equation based on the price contribution of each type:
[tex]\frac{2x \times 43 + 1x \times 67 + 5x \times P}{8x} = 96[/tex]
Here, [tex]P[/tex] is the price per kg of the third variety of rice.
Solve for [tex]P[/tex] by clearing the fraction:
First, eliminate [tex]x[/tex] by multiplying both sides by 8x:
[tex]2x \times 43 + 1x \times 67 + 5x \times P = 96 \times 8x[/tex]
Simplifying, we get:
[tex]86x + 67x + 5xP = 768x[/tex]
Combine like terms:
[tex]153x + 5xP = 768x[/tex]
Isolate [tex]P[/tex]:
Subtract 153x from both sides:
[tex]5xP = 768x - 153x[/tex]
[tex]5xP = 615x[/tex]
Divide through by 5x:
[tex]P = \frac{615}{5}[/tex]
Thus,
[tex]P = 123[/tex]
Therefore, the price per kg of the third variety of rice is ₹123.
The correct option is C) 123.
