In an examination,70 % of the candidates pass | vedclass

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(C) Let the total number of candidates be $100$.Percentage of candidates who passed in English $= 70 \%$.Percentage of candidates who failed in Englis

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(C) Let the total number of candidates be $100$.Percentage of candidates who passed in English $= 70 \%$.Percentage of candidates who failed in English $= 100 \% - 70 \% = 30 \%$.Percentage of candidates who passed in Mathematics $= 80 \%$.Percentage of candidates who failed in Mathematics $= 100 \% - 80 \% = 20 \%$.Percentage of candidates who failed in both subjects $= 10 \%$.Using the principle of inclusion-exclusion for failures:Percentage of candidates who failed in at least one subject $= (	ext{Failed in English}) + (	ext{Failed in Mathematics}) - (	ext{Failed in both})$$= 30 \% + 20 \% - 10 \% = 40 \%$.Therefore,the percentage of candidates who passed in both subjects $= 100 \% - 40 \% = 60 \%$.Given that $60 \%$ of the total candidates $= 144$.Let the total number of candidates be $x$.$0.60 	imes x = 144$$x = \frac{144}{0.60} = 240$.Thus,the total number of candidates is $240$.

In an examination,$70 \%$ of the candidates passed in English,$80 \%$ passed in Mathematics,and $10 \%$ failed in both subjects. If $144$ candidates passed in both,the total number of candidates was:

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