Find the ratio in which rice at Rs. 7.20 a kg be mixed with the rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg A] 3:2 B] 2:5 C] 3:4 D]4:3 Options : A B C D

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.

The cost price of a unit quantity of the mixture is Rs. 6.30/kg.

The cost price of the cheaper rice is Rs. 5.70/kg.

The cost price of the dearer rice is Rs. 7.20/kg.

Now, we subtract the cost price of the cheaper from the cost price of the mixture, and the cost price of the mixture from the cost price of the dearer.

So, 6.30 - 5.70 = 0.60 and 7.20 - 6.30 = 0.90

Therefore, the required ratio of the rice at Rs. 7.20/kg to the rice at Rs. 5.70/kg is 0.60 : 0.90, which simplifies to 2 : 3.

So, the correct answer is A] 3:2.

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 a given price should be mixed to produce a mixture of a desired price.

The cost price of a unit quantity of the mixture is the mean price. The mean price is always between the cost prices of two different types of items.

Here, the cost of 1 kg of cheaper rice is Rs. 5.70 and the cost of 1 kg of dearer rice is Rs. 7.20. The mean price is Rs. 6.30.

The rule of allegation states that the ratio in which the two types of items should be mixed is equal to the ratio of the differences between the cost prices of the two types of items and the mean price.

So, the difference between the cost of the dearer rice and the mean price is Rs. 7.20 - Rs. 6.30 = Rs. 0.90.

And the difference between the mean price and the cost of the cheaper rice is Rs. 6.30 - Rs. 5.70 = Rs. 0.60.

Therefore, the required ratio in which the two types of rice should be mixed is 0.90 : 0.60, which simplifies to 3 : 2.

So, the correct answer is A] 3:2.