Question

In a class, 52% of the students failed in English, 40% failed in Mathematics, and 20% failed in both the subjects. What percent of the students passed in both the subjects?

• A. 18%
• B. 28%
• C. 36%
• D. None of these

Hint:

Passed both = passed English + passed Maths minus passed at least one, and passed at least one equals 100% minus the percent who failed both.

Answer 1

The Correct Option is B

Step 1: Assume a convenient total number of students.
Since only percentages are given, assume the class has 100 students. This turns every percentage into a direct headcount, and the final answer as a percent stays the same.

Step 2: Mark the given numbers on a two-group diagram.
Failed in English = 52 students.
Failed in Mathematics = 40 students.
Failed in both = 20 students.

Step 3: Split each failing group into only-that-subject and both.
Failed English only \( = 52 - 20 = 32 \) students.
Failed Mathematics only \( = 40 - 20 = 20 \) students.
Failed both = 20 students, already counted once.

Step 4: Add up everyone who failed at least one subject.
Total who failed English only, Mathematics only, or both \( = 32 + 20 + 20 = 72 \) students.
This whole group could not pass both subjects together, since failing even one subject rules a student out.

Step 5: Subtract from the total to get the passed-both group.
Students who passed both subjects \( = 100 - 72 = 28 \), which out of 100 students is 28%.

Final Answer:
28% of the students passed in both English and Mathematics, the same answer as before, found this time by counting students directly instead of working with percentages algebraically. \[ \boxed{28\%} \]