Question

Sugar worth 15 per kg and 16 per kg is mixed with a third variety of some other cost in the ratio 1 : 1 : 2. If the mixture is of worth 20 per kg, what would be the cost of the third variety of sugar per kg?

• A. 15
• B. 19
• C. 20.5
• D. 22.5
• E. 24.5

Answer 1

Answer: (E)

Step 1: Understand the problem.
We are mixing three varieties of sugar with different costs. The first variety costs Rs. 15 per kg, the second variety costs Rs. 16 per kg, and the third variety costs \( x \) per kg. The mixture is made in the ratio 1:1:2, and the total cost of the mixture is Rs. 20 per kg. We need to find the cost \( x \) of the third variety of sugar.

Step 2: Set up the equation for the cost of the mixture.
The total cost of the mixture is the weighted average of the costs of the individual varieties. The formula for the weighted average cost is: \[ \text{Cost of Mixture} = \frac{(1 \times 15) + (1 \times 16) + (2 \times x)}{1 + 1 + 2} \] Simplifying the equation: \[ 20 = \frac{15 + 16 + 2x}{4} \] Multiply both sides by 4 to eliminate the denominator: \[ 80 = 15 + 16 + 2x \] Simplifying further: \[ 80 = 31 + 2x \] Solving for \( x \): \[ 2x = 80 - 31 = 49 \] \[ x = \frac{49}{2} = 24.5 \]

Step 3: Conclusion.
The cost of the third variety of sugar is Rs. 24.5 per kg.

Final Answer:
The correct option is (E): 24.5.