Problem: Three varieties of rice cost respectively 18, 25 and 28 Rs per kilo. Find a possible ratio in which the three could be mixed so that the resultant would be worth Rs 26 per kilo.

Solution:

To find the ratio in which three varieties of rice should be mixed so that the resultant mixture costs Rs 26 per kilo, we can use the alligation method.

Alligation method: It is a mathematical method used to find the ratio in which two or more ingredients with different prices should be mixed to give a desired price.

Steps:

1. Draw a line and mark the prices of the given ingredients on the line.
2. Find the difference between the given price and the desired price and mark it on the line.
3. The ingredients with higher prices should be placed on one side of the mark and the ingredients with lower prices should be placed on the other side of the mark.
4. The ratio in which the ingredients should be mixed is equal to the ratio of the distances of the ingredients from the mark.

Let's apply the alligation method to the given problem:



From the above diagram, we can see that the required ratio of the three varieties of rice should be 3:4:1.

Therefore, to get a mixture worth Rs 26 per kilo, we should mix 3 parts of the rice costing Rs 18 per kilo, 4 parts of the rice costing Rs 25 per kilo and 1 part of the rice costing Rs 28 per kilo.

Verification:

Let's verify if the above ratio is correct or not.

The cost of 1 kilo of the mixture = (3 * 18 + 4 * 25 + 1 * 28) / (3 + 4 + 1) = Rs 23

Since the cost of the mixture is Rs 23 per kilo, which is less than the desired price of Rs 26 per kilo, we need to add more of the rice costing Rs 28 per kilo to the mixture.

Let's say we add x kilos of rice costing Rs 28 per kilo to the mixture. Then, the cost of the mixture becomes:

(3 * 18 + 4 * 25 + x * 28) / (3 + 4 + x) = 26

Solving the above equation, we get x = 4/3

Therefore, the required ratio of the three varieties of rice is 3:4:1, and to get a mixture worth Rs 26 per kilo, we should mix 3 parts of the rice costing Rs 18 per kilo, 4 parts of the rice costing Rs 25 per kilo and 1.33 parts (approx) of the rice costing Rs 28 per kilo.