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 ?

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Submitted by examrobotsa on

Q: 141 (IAS/2000)
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 ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,10,11,4,10,5,2

keywords: 

{'mathematics': [0, 1, 0, 0], 'physics': [0, 2, 3, 4], 'examination': [0, 0, 1, 1], 'total number': [0, 0, 3, 0], 'many candidates': [0, 1, 0, 0], 'candidates': [3, 4, 1, 6], 'candidate': [1, 0, 0, 0]}

Let`s calculate the correct answer.

Given:

Percentage of candidates who took Physics = 65.8%

Percentage of candidates who took Mathematics = 59.2%

Total number of candidates = 2000

To find the number of candidates who took both Physics and Mathematics, we can use the formula:

Number of candidates who took both Physics and Mathematics = (Percentage of candidates who took Physics + Percentage of candidates who took Mathematics - Total percentage) * Total number of candidates

In this case, the total percentage is the sum of the percentages of Physics and Mathematics minus 100% (to avoid double counting the candidates who took both subjects).

Number of candidates who took both Physics and Mathematics = (65.8% + 59.2% - 100%) * 2000

Number of candidates who took both Physics and Mathematics = (125% - 100%) * 2000

Number of candidates who took both Physics and Mathematics = 25% * 2000

Number of candidates who took both Physics and Mathematics = 0.25 * 2000

Number of candidates who took both Physics and Mathematics = 500

Therefore, the correct answer is 500, which aligns with option (b).