Question

in an examination every candidate took Hindi or history or both 66% took Hindi and 59% took history the total number of a candidate was 3,000 how many candidate took both Hindi and history

Answer 1

Answer: The number of candidates who took both Hind and History is 750.

Step-by-step explanation:

Total candidates in the examination, n(A U B)= 100%

Total number of candidates= 3000 (given)

So,

100%= 3000

1%= 3000/100= 30

Now,

Candidates who took Hindi, n(A)= 66%

Candidates who took History, n(B)= 59%

Candidate who took both subjects= n(A intersection B)

Using the formula of union of sets, we see that

n(A U B)= n(A) +n(B) -n(A intersection B)

Rearranging the above expression, we get

n(A intersection B)= n(A) + n(B) - n(A U B)

n(A intersection B)=66% + 59% -100%

n(A intersection B)= 125% - 100%= 25%

We have,

1%= 30

So,

25%= 30*25= 750

Therefore, candidates who took both subjects= 750