Question
The letters of a certain six letter English meaningful
word are arranged from left to right in such a way that: (I) From the left end of the word, the first letter of the word is the third vowel as per the English alphabetical series. (II) The fourth letter from the left end of the word from the left end is the first vowel as per the English alphabetical series. (III) There are only two letters between the fourth letter and the fifth letter of the word (from the left end) as per the English alphabetical series. (IV) The second and third letter from the left end of the word are immediate preceding and immediate succeeding letter of letter 'O' and letter 'U' respectively as per the English alphabetical series. (V) The sixth letter from the left end is the immediate preceding letter of 'F' as per the English alphabetical series. If all the consonants of the word are replaced with its second succeeding letter and all the vowels are replaced with its third succeeding letter as per the English alphabetical series, then how many letters as per the English alphabetical series will be there between the fourth letter from the left end and the last letter from the left end after the rearrangement?Solution
Start with placing the first letter and the fourth letter to form the least possible cases. (I) From the left end of the word, the first letter of the word is the third vowel as per the English alphabetical series. The second vowel as per the English alphabetical series is 'I'. Thus, first letter from the left end is 'I'. (II) The fourth letter from the left end of the word from the left end is the first vowel as per the English alphabetical series. The first vowel as per the English alphabetical series is 'A'. Thus, fourth letter from the left end is 'A'. (III) There are only two letters between the fourth letter and the fifth letter of the word (from the left end) as per the English alphabetical series. The fourth letter is ‘A’ and fifth letter will be ‘D’. (IV) The second and third letter from the left end of the word are immediate preceding and immediate succeeding letter of letter 'O' and letter 'U' respectively as per the English alphabetical series. The second letter and third letter from the left end of the word are 'N' and ‘V’ respectively. (V) The sixth letter from the left end is the immediate preceding letter of 'F' as per the English alphabetical series. The sixth letter from the left end is ‘E’. So, the only meaningful English word possible is 'INVADE'. After replacing all the consonants of the word with its second succeeding letter and all the vowels with its third succeeding letter as per the English alphabetical series, we get: I          N        V        A        D        E L         P        X        D        F         H The fourth letter from the left end is 'D'. The last letter from the left end is 'H'. There are only three letters ('E', 'F', and 'G') between 'D' and 'H' as per the English alphabetical series.
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