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If “O” and “U”, irrespective of upper or lower case, occur exactly 504

June 1, 2025 by rawan239

If “O” and “U”, irrespective of upper or lower case, occur exactly 5040 times, then how many times does the letter “E” occur in the book in the upper or the lower case?

11840

11600

11430

11340

This question was previously asked in

UPSC CAPF – 2023

Download PDF Attempt Online

The correct answer is 11340. This question is known to be from a passage in the original paper that provided a rule for letter frequencies. Without the passage, the rule is not explicitly given. However, based on common interpretations and the correct answer from official sources for this specific question, the frequency of the vowel ‘E’ is approximately 9/4 times the frequency of ‘O’ or ‘U’.

Given that the letter “O” occurs exactly 5040 times and the letter “U” occurs exactly 5040 times, and assuming a relationship where N(E) / N(O) = 9/4 (or N(E) / N(U) = 9/4, which implies N(O)=N(U) as given), we can calculate the frequency of E.
N(E) = N(O) * (9/4)
N(E) = 5040 * (9/4)
N(E) = (5040 / 4) * 9
N(E) = 1260 * 9
N(E) = 11340.

The exact rule linking vowel frequencies to letter properties (like position in the alphabet) that results in the 9/4 ratio for E relative to O (or U) is not directly inferable from the question as presented. This implies the ratio was provided or derivable from the preceding passage in the original question paper. Common but unconfirmed postulations regarding the rule involve proportionality to (26 – alphabetical position) values or other complex relationships that are not straightforward.

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