Question

In an exam $60\%$ of the candidates passed in Maths and $70\%$ candidates passed in English and $20\%$ candidates failed in both subjects. If $2500$ candidates passed in both subjects. The total number of candidates appeared in the examination was

• A. $3000$
• B. $3500$
• C. $4000$
• D. $5000$

Answer 1

The correct option is D $5000$

According to question,

Candidates failed in english$=(100-60)\%=40\%$

Candidates failed in Mathematics$=(100-70)\%=30\%$

$20\%$ candidates failed in both.

candidates failed only in English$=(40-20)\%=20\%$

Candidates only failed in mathematics $=(30-20)\%=10\%$

Students passed in both subjects.

$=100-(20\%+20\%+10\%)=50\%$

Now

$50\%$ of the students$=2500$ (given)

So total students=$\frac{2500}{50}\times 100=5000$

Option $\text{D}$ is correct