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What is the percentage of candidates who are failing in second stage viva exam after clearing E2 exam in first stage ?

Three Venn diagrams of the selection results: the first stage of 100 candidates, the second stage for the 70 who cleared E1, and the second stage for the 60 who cleared E2, with the number of candidates in each region.

  • A.66·7%
  • B.75%
  • C.25%
  • D.33·3%

Answer: C

The percentage is 25%.

Use the diagram for the 60 candidates who cleared E2 in the first stage. Those who cleared the viva are 30 (cleared both) + 15 (cleared viva but failed E1) = 45.

\[ \begin{aligned} \text{failed viva} &= 60 - 45 = 15 \\ \text{percentage} &= \frac{15}{60} \times 100 = 25\% \end{aligned} \]

The 15 who failed are the 10 who cleared E1 but failed the viva and the 5 who failed both.

75% is the share who passed the viva. 66·7% is 40/60, the share who cleared E1, and 33·3% is 15/45, which compares the failures with those who passed instead of with all 60.

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