Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

To solve this problem, we can use the method of allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Here are the steps:

1. First, write down the cost of the cheaper and dearer ingredients, which are Rs. 5.70/kg and Rs. 7.20/kg respectively.

2. Write down the mean value, which is the cost of the mixture, Rs. 6.30/kg.

3. Calculate the differences between the cost of the cheaper ingredient and the mean value, and the cost of the dearer ingredient and the mean value. The difference should be taken in absolute values (ignoring if it is negative). So, the differences are |5.70 - 6.30| = 0.60 and |7.20 - 6.30| = 0.90.

4. The required ratio of the two ingredients is then given by the inverse ratio of these differences. So, the ratio in which the two types of rice should be mixed is 0.90 : 0.60, which simplifies to 3 : 2.

So, rice costing Rs. 7.20/kg should be mixed with rice costing Rs. 5.70/kg in the ratio 3:2 to produce a mixture worth Rs. 6.30/kg.

To solve this problem, we can use the method of allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Here are the steps:

1. First, write down the cost price of the cheaper and dearer ingredients, which are Rs. 5.70/kg and Rs. 7.20/kg respectively.

2. Write down the mean price, which is the cost price of the mixture, Rs. 6.30/kg.

3. Calculate the differences between the mean price and the prices of the cheaper and dearer ingredients. The difference between the mean price and the price of the cheaper ingredient is Rs. 6.30 - Rs. 5.70 = Rs. 0.60. The difference between the price of the dearer ingredient and the mean price is Rs. 7.20 - Rs. 6.30 = Rs. 0.90.

4. The required ratio of the quantities of the cheaper and dearer ingredients is the inverse of the differences calculated in step 3. So, the ratio is 0.90 : 0.60, which simplifies to 3 : 2.

So, rice at Rs. 7.20 a kg and rice at Rs. 5.70 a kg should be mixed in the ratio 3 : 2 to produce a mixture worth Rs. 6.30 a kg.