In an exam 70% passed in English 65% passed in Maths while 27% failed in both.If 248 candidates passed in both.Find the total number of candidates

Dear Vivek,

Solution:-Let the total no. of candidates are 'n'.

Then, no. of candidates passed in English (E) = 0.7n,

        no. of candidates passed in Maths (M) = 0.65n, and

        no. of candidates neither passed in English nor in Maths (E‾ ∩ M‾) = 0.27n.

[Here, E‾ and  M‾ are the complements of E and M respectively.]

        no. of candidates passed in both (E ∩ M) = 248

We know, (E U M) = n - (E‾ ∩ M‾) [Very standard formula]

and (E U M) = (E) + (M) - (E ∩ M) [Another standard formula]

These two formulas will give-

n - (E‾ ∩ M‾) = (E) + (M) - (E ∩ M)

n - 0.27n = 0.7n+0.65n - 248

n = 400 (Ans)

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Priyansh Bajaj