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?

To find the total number of students, we first determine the percentage of students who passed at least one paper. Since 15 percent failed both papers, 85 percent of the total students must have passed at least one paper.

Let A be the percentage who passed Paper I (70 percent) and B be the percentage who passed Paper II (60 percent). According to the formula for the union of two sets, the percentage who passed at least one paper equals the percentage who passed Paper I plus the percentage who passed Paper II minus the percentage who passed both.

Plugging in the values: 85 equals 70 plus 60 minus the percentage who passed both. This simplifies to 85 equals 130 minus the percentage who passed both. Therefore, the percentage of students who passed both papers is 45 percent.

The question states that 270 students passed both papers. If 45 percent of the total students equals 270, we can find the total by dividing 270 by 0.45. This calculation results in 600. Thus, the total number of students is 600. Correct option is A.