In what ratio must a grocer mix two varieties of pulses costing Rs.15 & Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 per kg?Options :3:75:77:37:5

This is a problem of mixtures and alligation. Alligation is a rule that allows us to find the ratio in which two or more ingredients at a given price must be mixed to produce a mixture of a desired price.

Here are the steps to solve this problem:

Step 1: Write down the cost of the cheaper and costlier ingredients on the two ends. Here, Rs.15/kg (cheaper pulse) and Rs.20/kg (costlier pulse).

Step 2: Write down the cost of the mixture in the middle. Here, Rs.16.50/kg.

Step 3: Calculate the differences between the cost of the mixture and the costs of the cheaper and costlier ingredients. The difference between Rs.16.50 and Rs.15 is Rs.1.50, and the difference between Rs.20 and Rs.16.50 is Rs.3.50.

Step 4: The required ratio of the two ingredients is the reciprocal of the differences calculated in step 3. So, the grocer must mix the two varieties of pulses in the ratio of 3.50 : 1.50, which simplifies to 7 : 3.

So, the correct option is 7:3.