More Questions from Simplification

There are 200 questions on a 3 hour examination. Among these questions are 50 Mathematics problems. It is suggested that twice as much time be spent on each Maths problem as for each other question. How many minutes should be spent on Mathematics problems?

Aptitude Simplification Difficulty: Medium
Choose an option
  • A
    36
  • B
    60
  • C
    72
  • D
    100

Answer

Correct Answer: 72

Explanation

### Concept & Formula\n\nThis problem requires setting up a linear equation based on time distribution. Total time available must equal the combined time spent on math questions and non-math questions.\n$$\\text{Total Time} = (N_{\\text{math}} \\times T_{\\text{math}}) + (N_{\\text{other}} \\times T_{\\text{other}})$$\n\n### Step-by-Step Solution\n\n* **Given:**\n * Total questions = 200\n * Mathematics questions = 50\n * Other questions = $200 - 50 = 150$\n * Total exam time = 3 hours = $3 \\times 60 = 180$ minutes\n\n* **Deduction:**\n Let the time spent on each non-math question be $x$ minutes.\n Therefore, the time spent on each mathematics problem is $2x$ minutes.\n\n* **Equation Setup:**\n $$(50 \\times 2x) + (150 \\times x) = 180$$\n $$100x + 150x = 180$$\n $$250x = 180$$\n $$x = \\frac{180}{250} = \\frac{18}{25}$$ minutes\n\n* **Target Calculation:**\n We need the total time spent on Mathematics problems, which is $50 \\times 2x = 100x$:\n $$\\text{Total Maths Time} = 100 \\times \\frac{18}{25} = 4 \\times 18 = 72 \\text{ minutes}$$\n\n### Exam Strategy & Shortcut\n\nUse the ratio method for time distribution:\n* Total relative weight for Maths = $50 \\times 2 = 100$\n* Total relative weight for Others = $150 \\times 1 = 150$\n* Total weight ratio = $100 : 150 = 2 : 3$\n\nMaths takes $\\frac{2}{2+3} = \\frac{2}{5}$ of the total exam time:\n$$\\text{Maths Time} = \\frac{2}{5} \\times 180 \\text{ minutes} = 2 \\times 36 = 72 \\text{ minutes}$$\n\n### Common Pitfall\n\nStudents often solve for $x$ (time per non-math question) or $2x$ (time per math question) and select that as the final answer, forgetting that the question asks for the **total** time spent on all 50 Mathematics problems.\n\n### Final Answer\n\n**Therefore, the correct answer is 72.**
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