These questions are based on the following information: 85 children went to an amusement park where they could ride on merry-go-round, roller coaster and Ferris wheel. It was known that 20 of them took all the three rides and 55 of them have taken at least two of the three rides. Each ride costs Re 1, and the total receipt of the amusement park was ₹ 145. How many children did not try any of the rides?

### Concept & Logic Following up on the previous calculation, the total number of children is the sum of children who took 0, 1, 2, and 3 rides. Once we have the subsets, finding the remainder is straightforward addition and subtraction. ### Step-by-Step Solution * **Given:** Total children = 85. * From previous analysis, we know the breakdown of rides: * Children taking exactly 3 rides: $n(3) = 20$ * Children taking exactly 2 rides: $n(2) = 35$ * Children taking exactly 1 ride: $n(1) = 15$ * **Calculation:** The sum of all categories must equal the total number of children. $$n(0) + n(1) + n(2) + n(3) = \text{Total Children}$$ $$n(0) + 15 + 35 + 20 = 85$$ * Sum the known values: $$n(0) + 70 = 85$$ * Isolate $n(0)$: $$n(0) = 85 - 70 = 15$$ * Thus, 15 children did not try any of the rides. ### Exam Strategy & Shortcut If you have already calculated that $n(1) = 15$ from the previous question, this step takes 5 seconds. Total children = 85. Active children = (Exactly 1) + (At least 2) = $15 + 55 = 70$. Inactive children = $85 - 70 = 15$. ### Common Pitfall Accidentally double counting the children who took 3 rides when trying to sum the groups. Remember that the "55" figure for "at least two rides" *already includes* the 20 who took three rides. ### Final Answer **Therefore, the correct answer is 15.**