Question

Rice of rate Rs. 126 per kg and Rs. 135 per kg and 3^rd variety are mixed in the ratio 1 : 1 : 2. If the final mixture is worth Rs. 153 per kg, what is the rate of the third variety per kg?

• A. 165.4
• B. 170
• C. 169
• D. 175.5

Hint:

Always assume simple values for ratios (like 1 kg, 1 kg, and 2 kg) to keep calculations straightforward.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem can be solved using the weighted average method for mixture allegations.
Key Formula or Approach:
Let the three quantities of rice mixed be in the ratio $1 : 1 : 2$ (representing $1\text{ kg}$, $1\text{ kg}$, and $2\text{ kg}$ respectively).
Let the price of the third variety be $P$ Rs/kg.
The weighted average price is: \[ \text{Average Price} = \frac{w_1 p_1 + w_2 p_2 + w_3 p_3}{w_1 + w_2 + w_3} \]

Step 2: Detailed Explanation:
Substitute the given values into the formula: \[ \frac{(1 \times 126) + (1 \times 135) + (2 \times P)}{1 + 1 + 2} = 153 \] \[ \frac{126 + 135 + 2P}{4} = 153 \] \[ 261 + 2P = 153 \times 4 \] \[ 261 + 2P = 612 \] Subtract 261: \[ 2P = 351 \] \[ P = 175.5 \text{ Rs/kg} \] Thus, the price of the third variety is Rs 175.5 per kg.

Step 3: Final Answer:
The price is Rs 175.5 per kg, which corresponds to Option (D).