Question

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 ?

• A. 2550
• B. 2800
• C. 3000
• D. 3200

Answer 1

The Correct Option is C

The problem involves calculating the total number of students who appeared in a competitive exam based on the information given about their test performance. To solve this, let's define the total number of students as \( N \).

According to the problem, 10% of the total students cleared all sections. This can be expressed as: 
\[ 0.10 \times N \]

Also, 5% of them cleared none of the sections: 
\[ 0.05 \times N \]

From the remaining students (85% of the total), different percentages cleared only specific sections:

30% cleared only section 1: 

\[ 0.30 \times 0.85N \]

20% cleared only section 2:

\[ 0.20 \times 0.85N \]

10% cleared only section 3:

\[ 0.10 \times 0.85N \]

Remaining cleared only section 4. Given as 1020 candidates.

The sum of candidates clearing only one specific section is equal to:

• \( 0.30 \times 0.85N + 0.20 \times 0.85N + 0.10 \times 0.85N + 1020 = 0.60 \times 0.85N + 1020 \)

Since the total for these students must be \( 0.85N \), we equate:

• \( 0.60 \times 0.85N + 1020 = 0.85N \)

Solving this equation:

• \( 0.60 \times 0.85N + 1020 = 0.85N \)
• \( 1020 = 0.85N - 0.51N \)
• \( 1020 = 0.34N \)
• \( N = \frac{1020}{0.34} \)
• \( N = 3000 \)

Thus, the total number of students who appeared in the competitive exam is 3000.