Rice worth ₹126 per kg and ₹135 per kg are mixed with a third variety in the ratio of 1:1:2. If the mixture is worth ₹153 per kg, then the price of the third variety per kg (in ₹) is:

​Given:

Price of the first variety of rice: ₹126 per kg

Price of the second variety of rice: ₹135 per kg

Ratio of the mixture: 1:1:2

Price of the mixture: ₹153 per kg

The weighted average formula for the price of the mixture:

​$$\text{Mixture Price} = \frac{(P_1 \times Q_1) + (P_2 \times Q_2) + (P_3 \times Q_3)}{Q_1 + Q_2 + Q_3}$$​​

Where:

$$P_1​, P_2​, P_3$$​​ are the prices per kg of the first, second, and third varieties respectively.

$$Q_1, Q_2​, Q_3$$​​ are the quantities (in kg) of the first, second, and third varieties respectively.

Let price of third variety = x
ATQ,
126$$\times 1$$​ + 135$$\times1$$​ + x$$\times2$$​ = 153×4 

2x = 612 - 261 
2x = 351
x = 175.5 

​$$\therefore$$ the price of the third variety of rice = ₹ 175.5.​