Question

in an examination 30% of the candidates failed in English 35% failed in GK and 27% failed in both the subjects if 310 candidates passed in both how many candidates appeared in the examination​

Answer 1

Answer:

Total number of candidates appeared in the examination is 500.

Step-by-step explanation:

A : The candidate failed in English is 30%.

B : The candidate failed in GK is 35%.

A∩B : The candidate failed in both English and GK is 27%.

The candidate failed in at-least one subject is

$A\cup B=A+B-A\cap BA∪B=A+B−A∩B$

$A\cup B=30\%+35\%-27\%A∪B=30%+35%−27%$

$A\cup B=38\%A∪B=38%$

Therefore 38% students failed in at-least one subject. The candidates passed in both is

$1-38\%=62\%1−38%=62%$

It is given that 310 candidates passed in both subjects. Let the total number of candidates appeared in the examination be x.

$x\times \frac{62}{100}=310x×10062=310$

$x=310\times \frac{100}{62}x=310×62100</p><p>x=500x=500$

Therefore, the total number of candidates appeared in the examination is 500.