Question:medium

80% of students of a class took Statistics and 45% took Mathematics. If each student took Statistics or Mathematics and 40 took both, the total number of students in the class was:

Updated On: Jul 15, 2026
  • 160
  • 180
  • 200
  • 225
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The Correct Option is A

Approach Solution - 1

Step 1: Understanding the Question.
We are told 80% of a class took Statistics, 45% took Mathematics, every student took at least one of the two subjects, and 40 students took both. We need the total number of students in the class.

Step 2: Key Formula or Approach.
For two groups that together cover everyone, the percentage taking both subjects equals the sum of the two percentages minus 100%, since students counted twice must be subtracted out to leave the whole class.
\[ \%(\text{both}) = \%(\text{Statistics}) + \%(\text{Mathematics}) - 100\% \]

Step 3: Detailed Explanation.
Putting in the given percentages:
\[ \%(\text{both}) = 80\% + 45\% - 100\% = 25\% \]
So 25% of the class took both subjects. This group has 40 students, so if \( x \) is the total class size:
\[ \frac{25}{100} \times x = 40 \]
\[ x = \frac{40 \times 100}{25} \]
\[ x = 160 \]

Step 4: Final Answer.
The total number of students in the class is 160. \[ \boxed{160} \]
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Approach Solution -2

Every student in the class took Statistics, Mathematics, or both, so the class can be split into three separate groups that add up to the whole: students who took only Statistics, students who took only Mathematics, and the 40 who took both. For any candidate total, the only-Statistics group is 80% of the total minus the 40 who took both, and the only-Mathematics group is 45% of the total minus the same 40. Adding these two groups to the 40 who took both must give back the exact total. Let's test each option this way.

  1. Option (A): 160: Statistics takers = \( 0.8 \times 160 = 128 \), so only-Statistics = \( 128 - 40 = 88 \). Mathematics takers = \( 0.45 \times 160 = 72 \), so only-Mathematics = \( 72 - 40 = 32 \). Adding the three groups: \( 88 + 32 + 40 = 160 \), which matches the total exactly.
  2. Option (B): 180: Statistics takers = \( 0.8 \times 180 = 144 \), only-Statistics = \( 144 - 40 = 104 \). Mathematics takers = \( 0.45 \times 180 = 81 \), only-Mathematics = \( 81 - 40 = 41 \). Adding: \( 104 + 41 + 40 = 185 \), which is more than the 180 total, so this option is inconsistent.
  3. Option (C): 200: Statistics takers = \( 0.8 \times 200 = 160 \), only-Statistics = \( 160 - 40 = 120 \). Mathematics takers = \( 0.45 \times 200 = 90 \), only-Mathematics = \( 90 - 40 = 50 \). Adding: \( 120 + 50 + 40 = 210 \), exceeding the 200 total, so this also fails.
  4. Option (D): 225: Statistics takers = \( 0.8 \times 225 = 180 \), only-Statistics = \( 180 - 40 = 140 \). Mathematics takers = \( 0.45 \times 225 = 101.25 \), which is not a whole number of students on its own, showing this option cannot represent a real class size.

Only the total of 160 splits cleanly into three whole-number groups, only-Statistics, only-Mathematics, and both, that add back up to the total itself.

Therefore, the correct answer is 160.

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