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What is the ratio of the “percentage of candidates clearing E2 exam in second stage after clearing E1 exam in first stage” to “percentage of candidates clearing E1 exam in second stage after clearing E2 exam in first stage” ?

Three Venn diagrams. First stage, 100 candidates: cleared E1 but failed E2 30, both 40, cleared E2 but failed E1 20. The 70 who cleared E1: E2 but not viva 10, both 30, viva but not E2 20. The 60 who cleared E2: E1 but not viva 10, both 30, viva but not E1 15.

  • A.\(\frac{4}{7} : \frac{2}{3}\)
  • B.\(\frac{3}{7} : \frac{2}{7}\)
  • C.\(\frac{4}{7} : \frac{3}{7}\)
  • D.\(\frac{3}{7} : \frac{1}{5}\)

Answer: A

The ratio is \(\frac{4}{7} : \frac{2}{3}\).

Read the two second-stage diagrams.

  • Of the 70 candidates who cleared E1 first, those who cleared E2 in the second stage are 10 + 30 = 40, a fraction of 40/70 = 4/7.
  • Of the 60 who cleared E2 first, those who cleared E1 in the second stage are 10 + 30 = 40, a fraction of 40/60 = 2/3.

The two percentages are therefore in the ratio 4/7 : 2/3.

The options beginning with 3/7 count only the 30 candidates who cleared both E2 and the viva, leaving out the 10 who cleared E2 but failed the viva. None of 3/7, 2/7 or 1/5 matches the 40 out of 60 in the other diagram.

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