In an examination, 62 \% of the candidates failed in English, 42%...

In an examination,

62 \%

of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is $In an examination, 62 \% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those$

Options

A $11$
B $16$
C $18$
DNone of these

Correct answer

B. $16$

Step-by-step solution

$In an examination, 62 \% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those$ From the given condition,

\mathrm{a}+\mathrm{c}=62 \mathrm{k} ; \mathrm{b}+\mathrm{c}=42 \mathrm{k}

and

\mathrm{c}=20 \mathrm{k}

Hence

\mathrm{a}=42 \mathrm{k}

and

\mathrm{b}=22 \mathrm{k}

Number of students who failed in none means passed in both

=\mathrm{n}=100 \mathrm{k}-(\mathrm{a}+\mathrm{b}+\mathrm{c})=100 \mathrm{k}-(42 \mathrm{k}+22 \mathrm{k}+20 \mathrm{k})=16 \mathrm{k}

. or

16 \%

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