SZF IOM · Achievers Section

Case Study and Application

Real-life data interpretation and modelling problems requiring multi-step reasoning.

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  • Q1 · Case Study and Application · MEDIUM

    A school is organizing a trip for 480 students. The transportation company offers two types of buses: Type X: Capacity 40 students, rental cost Rs 3000 per bus Type Y: Capacity 60 students, rental cost Rs 4200 per bus The school decides to use a combination of both types such that all students can travel and the total cost is minimized. If the school uses 4 buses of Type X, how many buses of Type Y are needed, and what is the total cost?

  • Q2 · Case Study and Application · MEDIUM

    A water tank has two inlet pipes A and B. Pipe A can fill the tank in 8 hours and pipe B in 12 hours. There is an outlet pipe C that can empty the full tank in 6 hours. If all three pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank completely?

  • Q3 · Case Study and Application · HARD

    A shopkeeper marks up the price of an item by 60% above cost price. During a festival sale, he offers a 25% discount on the marked price and still makes a profit of ₹280 on selling the item. What was the cost price of the item?

  • Q4 · Case Study and Application · EASY

    A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the journey. What is the original speed of the train?

  • Q5 · Case Study and Application · MEDIUM

    A school library charges a late fee using the formula F = 5 + 2(d-3) for d > 3 days, where d is the number of days late and F is the fee in rupees. For d ≤ 3, there is no fee. A student returned a book 8 days late. How much did they pay in late fees?

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