Question

In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of Students?

• A. $600$
• B. $580$
• C. $560$
• D. $540$

Answer 1

The correct option is A $600$

Venn diagram of failed student

$\Rightarrow$ Failed candidate in Paper $I=(100-70)\%=30\%$

$\Rightarrow$ Failed candidate in Paper $II=(100-60)\%=40\%$

We are going to draw a Venn diagram.

$\Rightarrow$ Percentage of passed students in both subject $=100-(15+15+25)=45\%$

Let total students be $x$.

According to the question,

$45\%$ of students total students $=270$

$\Rightarrow$ $\frac{45}{100}\times x=270$

$\Rightarrow$ $x=270\times \frac{100}{45}$

$\Rightarrow$ $x=600$

$\therefore$ Total number of students are $600$.