In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics?
- A750
- B500Correct
- C250
- D125
Explanation
To solve this problem, we use the principle of set theory for two overlapping groups.
The formula is: Total Percentage = (Percentage in Physics + Percentage in Mathematics) - Percentage in Both.
Since every candidate took at least one subject, the total percentage is 100 percent.
Plugging in the numbers: 100 = 65.8 + 59.2 - Percentage in Both 100 = 125 - Percentage in Both Percentage in Both = 125 - 100 = 25 percent.
Now, we calculate 25 percent of the total number of candidates, which is 2000. 25 percent of 2000 is 0.25 multiplied by 2000, which equals 500.
Therefore, 500 candidates took both Physics and Mathematics. The correct option is B.
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