In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 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. Write down the cost of the cheaper and dearer ingredients on the left side. In this case, Rs. 15 and Rs. 20.

2. Write down the mean value in the middle. In this case, Rs. 16.50.

3. Subtract the cost of the cheaper ingredient from the mean value, and the mean value from the cost of the dearer ingredient.

   Rs. 20 - Rs. 16.50 = Rs. 3.50 Rs. 16.50 - Rs. 15 = Rs. 1.50

4. The required ratio of the two ingredients is the ratio of these differences. So, the grocer must mix the two varieties of pulses in the ratio of 3.50 : 1.50, which simplifies to 7 : 3 when we divide both sides by 0.5.

So, the grocer must mix the two varieties of pulses in the ratio of 7 : 3 to get a mixture worth Rs. 16.50 per kg.