Question

85 children went to an amusement park with 3 rides. Each ride costs Re.1. 20 children took all 3 rides, 55 took at least 2 rides, and the total receipt was Rs.145. How many children did not take any rides?

• A. 5
• B. 10
• C. 15
• D. 20

Hint:

Use total revenue and ride-based cost to back-calculate the number of children per group.

Answer 1

The Correct Option is C

Let: - \( a = \) number of children who took exactly 1 ride - \( b = \) number of children who took exactly 2 rides - \( c = \) number of children who took all 3 rides = 20 - Total number of children = 85 - Total money collected = 145 (each ride costs Re.1) Also, it's given that 55 children took at least 2 rides, i.e., \[ b + c = 55 b = 55 - 20 = 35 \] Now total ride revenue: Each child who took 1 ride paid Re.1 → total from them = \( a \) Each who took 2 rides paid Rs.2 → total from them = \( 2b = 70 \) Each who took 3 rides paid Rs.3 → total = \( 3c = 60 \) Total revenue: \[ a + 2b + 3c = 145 a + 70 + 60 = 145 a = 15 \] So, children who took at least one ride: \[ a + b + c = 15 + 35 + 20 = 70 \] Children who took no ride: \[ 85 - 70 = \boxed{15} \]