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?

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Q: 7 (IAS/2008)
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?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,7,5,5,2,0

keywords: 

{'paper ii': [0, 0, 1, 0], 'total number': [0, 0, 3, 0], 'students': [0, 1, 1, 1], 'examination': [0, 0, 1, 1], 'papers': [1, 0, 1, 1]}

Let`s solve the problem step by step to find the total number of students.

Let`s assume the total number of students is "x".

Given information:

- 70% of the students passed in Paper I. So, the number of students who passed Paper I is 70% of x, which is 0.7x.

- 60% of the students passed in Paper II. So, the number of students who passed Paper II is 60% of x, which is 0.6x.

- 15% of the students failed in both papers. So, the number of students who failed in both papers is 15% of x, which is 0.15x.

- 270 students passed in both papers.

Now, let`s analyze the information given:

From the given information, we can form the following equation:

Number of students who passed in Paper I + Number of students who passed in Paper II - Number of students who passed in both papers + Number of students who failed in both papers = Total number of students

0.7x + 0.6x - 270 + 0.15x = x

Combining like terms, we have:

1.45x - 270 = x

Simplifying the equation, we get:

0.45x = 270

Dividing both sides of the equation by 0.45, we have:

x = 270 / 0.45

Calculating this value, we find:

x = 600

Therefore, the total number of students is 600.

So, the correct option is Option 1: 600.

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