How to solve a mixture problem involving the cost of rice?

When a dealer mixes two types of rice, the cost of the resulting mixture will depend on the cost of the individual types of rice and the proportion in which they are mixed. Let's consider the following problem:

A dealer mixes rice costing Rs.13.84 with rice costing Rs.X per kg in the ratio 3:2 to get a mixture costing Rs.13.20 per kg. Find the value of X.

Step 1: Set up the equation

Let's assume that the dealer mixes 3 kg of the first type of rice costing Rs.13.84 per kg with 2 kg of the second type of rice costing Rs.X per kg. The resulting mixture weighs 5 kg and costs Rs.13.20 per kg. We can set up the following equation:

(3 * 13.84) + (2 * X) = 5 * 13.20

Simplifying this equation, we get:

41.52 + 2X = 66

2X = 24.48

X = 12.24

Therefore, the value of X is Rs.12.24 per kg.

Step 2: Check the answer

We can verify our answer by calculating the cost of the two types of rice and the resulting mixture. When the dealer mixes 3 kg of rice costing Rs.13.84 per kg with 2 kg of rice costing Rs.12.24 per kg, the total cost of the rice is:

(3 * 13.84) + (2 * 12.24) = 41.52 + 24.48 = 66

The resulting mixture weighs 5 kg and costs Rs.13.20 per kg, so the total cost of the mixture is:

5 * 13.20 = 66

Therefore, our answer is correct.

Conclusion

To solve a mixture problem involving the cost of rice, we need to set up an equation based on the proportion in which the two types of rice are mixed and the resulting cost of the mixture. We can then solve the equation to find the value of the unknown variable. It is important to check our answer by calculating the cost of the two types of rice and the resulting mixture to ensure that our solution is correct.