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Question

In an examination, every candidate took either Physics or Mathematics or both $$84\%$$ of the candidates took Physics and candidates who took Mathematics were half of those who took Physics. The total number of candidates being $$1000$$, how many took both Physics and Mathematics?


A
200
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B
240
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C
250
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D
260
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Solution

The correct option is D $$260$$
$$n(P\cup M) =100\%, n(M) = 42\%, n(P) = 84\%$$
$$n(P\cap M) = n(M) + n(P) - n(P\cup M)$$
= $$42+84-100 = 26\%$$
Number of Candidates who have taken both
= $$\dfrac{26}{100}\times1000=260$$

Mathematics

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