A 3-hour (180-minute) exam has 200 questions: 50 Mathematics, 100 General Knowledge, and 50 Science. Ram spends twice as much time per Mathematics question as he spends per each non-Mathematics question. How many total minutes does he spend on Mathematics questions?

Introduction / Context:This time-allocation problem checks proportional reasoning. You are told that the per-question time for Mathematics is exactly twice that for each other subject. With the total time fixed, you can set up a simple equation in one variable to find the duration spent on Mathematics.

Given Data / Assumptions:

• Total exam time = 3 hours = 180 minutes.
• Question counts: 50 Mathematics, 100 General Knowledge, 50 Science (total non-Mathematics = 150).
• Time per Mathematics question is twice time per non-Mathematics question.

Concept / Approach:Let t be the time in minutes per non-Mathematics question. Then each Mathematics question takes 2t minutes. Multiply these by the respective quantities of questions to build the total time equation. Solve for t and then compute the time on Mathematics only.

Step-by-Step Solution:

Verification / Alternative check:Time on non-Mathematics = 150 * 0.72 = 108 minutes. 72 + 108 = 180 minutes, which matches the total exam time, verifying correctness.

Why Other Options Are Wrong:36 and 60 assume wrong multipliers or miscount questions. 100 and 80 result from setting the double rate incorrectly or forgetting total time is only 180 minutes.

Common Pitfalls:Using the same per-question time across subjects, ignoring that Mathematics takes double time, or mixing up total question counts when forming the equation.

Final Answer:72