Question

In a certain examination 77 p.c. pass in English and 34 p.c. fail in Mathematics. If 13 p.c. fail in both subjects and 784 passes in both the subjects. Find the total number of candidates.
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Answer 1

Since, passed in English = $77\%$
$\therefore$ failed in English = $(100-77)\%=23\%$
Now, failed in both = $13\%$
$\therefore$ failed only in English = $(23-13)\%=10\%$
$\therefore$ Total failure = failed in both + failed only in English + failed only in Mathematics.
$=13\%+10\%+21\%$
$=44\%$
Hence, passed in both = $(100-44)\%=56\%$
Thus $56\%$ of total number of candidates = 784
$\therefore$ $100\%$ of total number of candidates = $\frac{784}{56}\times 100$
= 1400
$\therefore$ Total number of candidates = 1400