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's solve the problem step-by-step by following the instructions given in the question.

Step 1: Identify the original word and its vowels
The given word is TRANSLATION.
Let's list the positions of all letters from left to right:

1st letter: T
2nd letter: R
3rd letter: A (1st vowel)
4th letter: N
5th letter: S
6th letter: L
7th letter: A (2nd vowel)
8th letter: T
9th letter: I (3rd vowel)
10th letter: O (4th vowel)
11th letter: N

Step 2: Replace vowels with the specified letters
Replacing the 1st, 2nd, 3rd, and 4th vowels (from left to right) with 'M', 'H', 'Y', and 'F' respectively:

- 1st vowel 'A' (at position 3) is changed to M
- 2nd vowel 'A' (at position 7) is changed to H
- 3rd vowel 'I' (at position 9) is changed to Y
- 4th vowel 'O' (at position 10) is changed to F

The new word formed is: T R M N S L H T Y F N

Step 3: Analyze the 7th letter from the left end
The 7th letter from the left end in the new word is H.
The alphabetical position (numerical value) of letter H in the English alphabet is:

$Numerical\; value\; of\; H=8$

Half of this numerical value is:

$\frac{8}{2}=4$

Step 4: Find the pairs of letters according to the alphabetical series
A pair of letters has as many letters between them in the word as in the English alphabetical series (in both forward and backward directions).

Let's map each position in the new word to its corresponding alphabetical rank:

1. T (20)
2. R (18)
3. M (13)
4. N (14)
5. S (19)
6. L (12)
7. H (8)
8. T (20)
9. Y (25)
10. F (6)
11. N (14)

Checking for pairs whose position difference matches their alphabetical distance:

1. M (3rd letter) and N (4th letter):
Distance in word = 4 - 3 = 1
Alphabetical distance = 14 - 13 = 1 (Pair: MN)

2. N (4th letter) and L (6th letter):
Distance in word = 6 - 4 = 2
Alphabetical distance = 14 - 12 = 2 (Pair: N-L, backward direction)

3. M (3rd letter) and F (10th letter):
Distance in word = 10 - 3 = 7
Alphabetical distance = 13 - 6 = 7 (Pair: M-F, backward direction)

4. R (2nd letter) and Y (9th letter):
Distance in word = 9 - 2 = 7
Alphabetical distance = 25 - 18 = 7 (Pair: R-Y, forward direction)

Conclusion:
There are a total of 4 such letter pairs.
Since 4 is equal to half of the numerical value of the 7th letter ('H', whose value is 8), the number of pairs is Equal to half of the numerical value of the 7th letter from left end in the new word.