Question

In a certain exam, \((\frac{1}{10})^{th}\) of the students passed by 1^st division, \((\frac{1}{4})^{th}\) of the students passed by 2^nd division, and half of the students passed by 3^rd division. If the remaining 54 students failed in the exam, then what was the total number of students who appeared in the exam?

• A. 320
• B. 340
• C. 360
• D. 380

Answer 1

The Correct Option is C

Step 1: Let the total number of students be x.

• Students who passed 1st division: x/10
• Students who passed 2nd division: x/4
• Students who passed 3rd division: x/2 

Step 2: Total number of students who passed:

• x/10 + x/4 + x/2

Find a common denominator:

• x/10 + 5x/20 + 10x/20 = 2x/20 + 5x/20 + 10x/20 = 17x/20

Step 3: Students who failed:

• x − 17x/20 = 3x/20

We are told that the number of students who failed is 54, so:

• 3x/20 = 54 ⇒ x = 54 × 20

Conclusion: The total number of students who appeared in the exam is 360.