Question:medium
In a competitive exam there were 5 sections. 10% of the total number of students cleared the cut off in all the sections and 5% cleared none of the sections. From the remaining candidates 30% cleared only section 1, 20% cleared only section 2, 10% cleared only section 3 and remaining 1020 candidates cleared only section 4. How many students appeared in the competitive exam?
In a competitive exam there were 5 sections. 10% of the total number of students cleared the cut off in all the sections and 5% cleared none of the sections. From the remaining candidates 30% cleared only section 1, 20% cleared only section 2, 10% cleared only section 3 and remaining 1020 candidates cleared only section 4. How many students appeared in the competitive exam?
Show Hint
Subtract the fixed percentages first, then split the remaining group by the given shares.
Updated On: Jul 16, 2026
- 2550
- 2800
- 3000
- 3200
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: Work entirely in percentages of the total, call it T.
Students who cleared all sections or none of the sections together make up $10\% + 5\% = 15\%$ of $T$. So the remaining students are $100\% - 15\% = 85\%$ of $T$.
Step 2: Find what fraction of the whole exam clears only section 4.
Section 4 only takes up $100\% - 30\% - 20\% - 10\% = 40\%$ of the remaining group. As a share of the whole exam this is $40\% \times 85\% = 34\%$ of $T$.
Step 3: Solve for T using the given number.
We are told this 34% share equals 1020 students, so $0.34T = 1020$, giving $T = \frac{1020}{0.34} = 3000$.
Final Answer:
Working directly in percentages of the whole exam also gives 3000 students. \[ \boxed{3000} \]
Students who cleared all sections or none of the sections together make up $10\% + 5\% = 15\%$ of $T$. So the remaining students are $100\% - 15\% = 85\%$ of $T$.
Step 2: Find what fraction of the whole exam clears only section 4.
Section 4 only takes up $100\% - 30\% - 20\% - 10\% = 40\%$ of the remaining group. As a share of the whole exam this is $40\% \times 85\% = 34\%$ of $T$.
Step 3: Solve for T using the given number.
We are told this 34% share equals 1020 students, so $0.34T = 1020$, giving $T = \frac{1020}{0.34} = 3000$.
Final Answer:
Working directly in percentages of the whole exam also gives 3000 students. \[ \boxed{3000} \]
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