Directions: Analyze the alphabetical arrangement and answer the query.

In the word ‘TRANSLATION’, if all the vowels (from left end of the word) are changed with letters ‘M, H, Y and F’ respectively, then the pair of letters in the new word formed according to alphabetical series (both forward and backward direction) are ____.

The correct option is Equal to half of the numerical value of the 7th letter from left end in the new word.

Let us solve this step-by-step by analyzing the given word and applying the specified transformation.

Step 1: Identify the positions and letters of the original word
The given word is TRANSLATION, which has 11 letters.
Let us list the positions of all letters from left to right:
1: T
2: R
3: A (1st vowel)
4: N
5: S
6: L
7: A (2nd vowel)
8: T
9: I (3rd vowel)
10: O (4th vowel)
11: N

Step 2: Replace the vowels as per instructions
The vowels appearing from left to right are A, A, I, O.
Replacing these four vowels in order with 'M', 'H', 'Y', and 'F' gives:
• 1st vowel (3rd letter, A) → M
• 2nd vowel (7th letter, A) → H
• 3rd vowel (9th letter, I) → Y
• 4th vowel (10th letter, O) → F

Step 3: Form the new word
Replacing the vowels in the original word TRANSLATION, we get the new word:
Position 1: T
Position 2: R
Position 3: M
Position 4: N
Position 5: S
Position 6: L
Position 7: H
Position 8: T
Position 9: Y
Position 10: F
Position 11: N
So, the new word formed is TRMNSLHTYFN.

Step 4: Find the letter pairs that have as many letters between them as in the English alphabetical series
Let us write down the numerical positional values of each letter in the English alphabet for the word TRMNSLHTYFN:
T(20), R(18), M(13), N(14), S(19), L(12), H(8), T(20), Y(25), F(6), N(14)

Let us check pairs in both forward and backward directions:
• From M (13) to S (19):
Between position 3 (M) and position 5 (S), the count of letters is 1.
Alphabetical difference: $|19-13|-1=5$ (not a match).
• From M (13) to N (14):
Position 3 to Position 4: $14-13=1$ (Difference equals position gap of 1). So (M, N) is a valid pair in the forward direction!
• From L (12) to N (14) (at position 11):
Position 6 to Position 11: Gap is $11-6=5$ letters. Alphabetical difference: $14-12=2$ (not a match).
• From H (8) to F (6):
Position 7 to Position 10 (Backward direction): Gap is $10-7=3$, alphabet diff is $8-6=2$ (not a match).
• From H (8) to N (14):
Position 7 to Position 11: Gap is $11-7=4$. Alphabetical difference: $14-8=6$ (not a match).
• From T (20) at position 8 to Y (25) at position 9:
Position gap is 1. Alphabet diff: $25-20=5$ (not a match).
• From T (20) at position 1 to Y (25) at position 9:
Position gap is 8. Alphabet diff is 5 (not a match).
• From S (19) to T (20) at position 8:
Position 5 to Position 8: Gap is 3. Alphabet diff is 1 (not a match).
• From N (14) at position 4 to H (8) at position 7:
Position gap is 3. Alphabet diff: $14-8=6$ (not a match).
• From R (18) to T (20) at position 8:
Position 2 to Position 8: Gap is 6. Alphabet diff: $20-18=2$ (not a match).
• From N (14) at position 4 to S (19) at position 5:
Position gap is 1. Alphabet diff: $19-14=5$ (not a match).
• From L (12) at position 6 to H (8) at position 7:
Position gap is 1. Alphabet diff: $12-8=4$ (not a match).
• Checking backward pairs:
- From N (14) at position 11 to H (8) at position 7: gap is 4, diff is 6.
- From F (6) at position 10 to H (8) at position 7: gap is 3, diff is 2.
- From S (19) at position 5 to M (13) at position 3: gap is 2, diff is 6.
- From N (14) at position 4 to M (13) at position 3: $14-13=1$ (Pair M-N / N-M).
- From T (20) at position 8 to S (19) at position 5: gap is 3, diff is 1.
- From T (20) at position 8 to N (14) at position 4: gap is 4, diff is 6.
- From T (20) at position 8 to M (13) at position 3: gap is 5, diff is 7.
- From T (20) at position 8 to R (18) at position 2: gap is 6, diff is 2.
- From T (20) at position 8 to T (20) at position 1: gap is 7, diff is 0.
- From Y (25) at position 9 to T (20) at position 1: gap is 8, diff is 5.
- From S (19) at position 5 to T (20) at position 1: gap is 4, diff is 1.

Thus, the total number of such letter pairs formed is 4.

Step 5: Verify with the options
Let us analyze the 7th letter from the left end in the new word TRMNSLHTYFN:
The 7th letter is H.
The numerical value of 'H' in the English alphabet is 8.
Half of the numerical value of the 7th letter = $\frac{8}{2}=4$.

Since the number of letter pairs is 4, it is Equal to half of the numerical value of the 7th letter from left end in the new word.