Proportional Reasoning-1Class 8 Mathematics Case Study Questions

A school is organizing its annual trip. Last year, 3 buses were hired for a total of 162 students and teachers. All the buses were filled to capacity. This year, the number of participants has increased to 204. The school needs to determine the number of buses required and the associated costs, ensuring the same ratio of people per bus is maintained for safety and comfort. The cost of hiring one bus is ₹5,000. The school also has a policy to maintain a teacher-to-student ratio of approximately $1:17$ on all trips.

Kesang and her friend decide to run a lemonade stand. Their recipe for one batch, which makes 6 glasses of lemonade, requires 10 spoons of sugar and 3 lemons. They sell each glass for ₹15. For an upcoming fete, they plan to make a much larger quantity. They start with an initial investment for sugar and lemons, which they put in as a ratio of $2:1$ respectively. They estimate they will sell at least 48 glasses of lemonade during the fete.

A mason is hired to build a compound wall around a rectangular plot. Based on his experience, building a wall of 10 feet in length requires approximately 1450 bricks and 2 bags of cement, assuming a standard height and thickness. The plot for the new wall has a length of 60 feet and a breadth of 40 feet. The mason needs to calculate the total materials required for the job to provide a cost estimate. He wants to ensure that the ratio of materials used per foot of wall is consistent throughout the project to maintain uniform strength.