Question

In examination , 30% of the candidates fail in English, 35% in Gk and 27% failed in both the subject. If 310 candidates passed in both, how many candidates appeared in the examination

Answer 1

Answer:

The total candidates appeared in exam = 500

Step-by-step explanation:

Given :

30% of the candidates fail in English

35% in Gk

27% failed in both the subject.

Solution:

We have formula :

A∪B=A+B-A∩B

A U B is the event that either A or B or both occur. • A n B is the event that both A and B occur at the same time.

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%.

A∪B = The candidate failed in at-least one subject

Putting values in fromula:

⇒A∪B=30%+35%-27%

⇒A∪B=38%

The candidates passed in both is 100%-38% = 62%

Since we are given that  310 candidates passed in both

Let x be the total no. of candidates.

⇒$\frac{62}{100}x = 310$

⇒$\frac{310*100}{62} = x$

⇒$500 = x$

Thus , The total candidates appeared in exam = 500