Question:
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:
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
The correct option is (A): 160.
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Approach Solution -2
This question wants the total number of students in a class where 80% take Statistics, 45% take Mathematics, every student takes at least one of the two, and 40 students take both. We can check each option by testing whether 25% of that total equals 40, since the students who take both subjects make up 80% + 45% - 100% = 25% of the class.
- Option (A): 160: 25% of 160 works out to 40. This matches the number of students who take both Statistics and Mathematics exactly, so 160 fits every condition in the question.
- Option (B): 180: 25% of 180 works out to 45, not 40. A class of 180 would need 45 students taking both subjects, more than the 40 given, so this option does not fit.
- Option (C): 200: 25% of 200 works out to 50. This is well above the 40 students stated in the question, so 200 is too large a class size.
- Option (D): 225: 25% of 225 works out to 56.25, not even a whole number of students, and far above 40. This option can be ruled out on both counts.
Only 160 satisfies the condition that 25% of the class equals the 40 students who took both subjects.
Therefore, the correct answer is 160.
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Approach Solution -3
This question gives the total class as unknown, with every student taking at least one of Statistics or Mathematics, so the class splits into three non-overlapping groups: students who took only Statistics, students who took only Mathematics, and the 40 students who took both. Let \( T \) be the total number of students. Since 80% of \( T \) took Statistics and 45% of \( T \) took Mathematics, and everyone took at least one subject, by inclusion-exclusion the number taking both is \( 0.8T + 0.45T - T = 0.25T \). Setting this equal to the given 40 students, \( 0.25T = 40 \), so \( T = 160 \). Let's check each option against this equation to confirm.
- Option (A): 160: Substituting \( T = 160 \) into \( 0.25T \) gives \( 0.25 \times 160 = 40 \), which exactly matches the 40 students who took both subjects. This value satisfies the equation derived from inclusion-exclusion.
- Option (B): 180: Substituting \( T = 180 \) gives \( 0.25 \times 180 = 45 \), meaning a class of this size would need 45 students taking both subjects, not the 40 stated, so this value does not satisfy the equation.
- Option (C): 200: Substituting \( T = 200 \) gives \( 0.25 \times 200 = 50 \) students taking both, ten more than given, so this overshoots the required count and fails the equation.
- Option (D): 225: Substituting \( T = 225 \) gives \( 0.25 \times 225 = 56.25 \), which is not even a whole number of students, ruling this out immediately.
Only \( T = 160 \) satisfies the equation \( 0.25T = 40 \) obtained from inclusion-exclusion of the two subject groups.
Therefore, the correct answer is 160.
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