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
B
240
C
250
D
260

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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