Question:
In a certain exam, \((\frac{1}{10})^{th}\) of the students passed by 1st division, \((\frac{1}{4})^{th}\) of the students passed by 2nd division, and half of the students passed by 3rd division. If the remaining 54 students failed in the exam, then what was the total number of students who appeared in the exam?
In a certain exam, \((\frac{1}{10})^{th}\) of the students passed by 1st division, \((\frac{1}{4})^{th}\) of the students passed by 2nd division, and half of the students passed by 3rd division. If the remaining 54 students failed in the exam, then what was the total number of students who appeared in the exam?
Updated On: Mar 5, 2025
- 320
- 340
- 360
- 380
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The Correct Option is C
Solution and Explanation
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.
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