In a 3-hour examination containing 150 questions, 50 questions are of type A and each type A question requires twice as much time as each type B question. How many minutes should a candidate spend on type A questions to complete the exam in the allotted time?

Introduction / Context:
This question is about time management in an examination. We are given total available time, total number of questions and a relationship between the time required for two types of questions. The goal is to determine how much time should be devoted to one type of question. This is a typical exam-planning and average-time-per-question problem that also reinforces the idea of relative time requirements.

Given Data / Assumptions:

Total exam duration = 3 hours = 180 minutes.
Total number of questions = 150.
Number of type A questions = 50.
Number of type B questions = 150 - 50 = 100.
Each type A question takes twice as much time as each type B question.
We assume the candidate uses the full 180 minutes efficiently.

Concept / Approach:
Let the time taken per type B question be t minutes. Then, by the given condition, the time taken per type A question is 2t minutes. We can express the total exam time as the sum of the time spent on all type A and type B questions in terms of t. Then equate that total to 180 minutes, solve for t, and finally compute the total time spent on all type A questions, which is 50 * 2t.

Step-by-Step Solution:
Step 1: Let time per type B question be t minutes. Step 2: Time per type A question is twice that, so it is 2t minutes. Step 3: Compute total time in terms of t. There are 50 type A questions, so time for them = 50 * 2t = 100t. There are 100 type B questions, so time for them = 100 * t = 100t. Step 4: Total exam time = time for type A + time for type B. Total time = 100t + 100t = 200t. Step 5: Set this equal to the given total time of 180 minutes. 200t = 180. Step 6: Solve for t. t = 180 / 200 = 0.9 minutes per type B question. Step 7: Time per type A question = 2t = 2 * 0.9 = 1.8 minutes. Step 8: Total time for all type A questions = 50 * 1.8 = 90 minutes.

Verification / Alternative check:
If 90 minutes are spent on type A questions, then 180 - 90 = 90 minutes remain for type B questions. With 100 type B questions, that gives 90 / 100 = 0.9 minutes for each type B question. Type A questions require twice this time: 1.8 minutes each. For 50 type A questions, this is 90 minutes, and for 100 type B questions, it is 90 minutes, summing to 180 minutes, which matches the total exam duration. This confirms our answer.

Why Other Options Are Wrong:
75 minutes for type A would leave 105 minutes for type B, which would imply inconsistent time per question compared with the twice-as-much condition.
82 minutes or 101 minutes also fail to satisfy both the total time and the exact 2:1 time ratio between question types.
60 minutes for type A would leave 120 minutes for type B, making type B questions much longer than allowed by the 2:1 condition.

Common Pitfalls:
Students often try to assign arbitrary times to each question without using the ratio information correctly. Another mistake is to divide total time by total number of questions directly and ignore the fact that type A questions take double the time. Some may also misinterpret twice as much as adding a fixed amount instead of multiplying. Always set a variable for the smaller time and then use the ratio to express the larger time before writing the total time equation.

Final Answer:
The candidate should spend 90 minutes on type A questions.