In a survey of 170 people, it has been found that 90 eatidly, 85 eat vada and 65 eat dosA. 50 eat idly &vada, 30eat vada&dosa, 40 eat idly &dosa and 20 eat all the three. How many eat exactly two of the varieties?a.60b.80c.70d.40

To solve this problem, we need to understand that the total number of people who eat exactly two varieties is the sum of the people who eat each pair of varieties minus twice the number of people who eat all three (since they are counted in each pair).

Here are the steps to solve the problem:

1. Calculate the total number of people who eat each pair of varieties:

   • Idly and Vada: 50
   • Vada and Dosa: 30
   • Idly and Dosa: 40 The total is 50 + 30 + 40 = 120.

2. Calculate the number of people who eat all three varieties, which is 20. Since these people are counted in each pair, we need to subtract them twice from the total. So, 20 * 2 = 40.

3. Subtract the number of people who eat all three varieties from the total number of people who eat each pair of varieties: 120 - 40 = 80.

So, the number of people who eat exactly two of the varieties is 80 (option b).