In a code language, 'HOPE' is coded as ‘FRRL’ and 'TAIL' is coded as ‘MKDX’. How will 'STORY' be coded in the same language?

The correct option is ZTRXX.

Let's analyze the coding pattern by looking at how the letters of the words are transformed in the given examples.

Example 1: 'HOPE' is coded as 'FRRL'
Let's find the position of each letter in the standard English alphabet (A = 1, B = 2, ..., Z = 26):
H (8) → F (6) : Difference is 6 - 8 = -2
O (15) → R (18) : Difference is 18 - 15 = +3
P (16) → R (18) : Difference is 18 - 16 = +2
E (5) → L (12) : Difference is 12 - 5 = +7
This pattern of changes (-2, +3, +2, +7) doesn't seem highly regular. Let's look closely at the reverse mapping or alternative shifts. Let's write the word 'HOPE' and its code 'FRRL' reverse-aligned or check cross-patterns:
H (8) → L (12) : +4
O (15) → R (18) : +3
P (16) → R (18) : +2
E (5) → F (6) : +1
Yes! The letters of the word 'HOPE' are coded in reverse order with a sequential increment:
• The last letter 'E' (5) + 1 = 6 ('F')
• The third letter 'P' (16) + 2 = 18 ('R')
• The second letter 'O' (15) + 3 = 18 ('R')
• The first letter 'H' (8) + 4 = 12 ('L')
This gives the code 'FRRL'.

Example 2: 'TAIL' is coded as 'MKDX'
Let's apply the same reverse pattern with increments (+1, +2, +3, +4) to 'TAIL':
• The last letter 'L' (12) + 1 = 13 ('M')
• The third letter 'I' (9) + 2 = 11 ('K')
• The second letter 'A' (1) + 3 = 4 ('D')
• The first letter 'T' (20) + 4 = 24 ('X')
This gives the code 'MKDX'. The pattern is verified!

Applying the pattern to 'STORY':
The word has 5 letters: S, T, O, R, Y.
We apply the sequential increments (+1, +2, +3, +4, +5) starting from the last letter to the first:
• The 5th letter 'Y' (25) + 1 = 26 ('Z')
• The 4th letter 'R' (18) + 2 = 20 ('T')
• The 3rd letter 'O' (15) + 3 = 18 ('R')
• The 2nd letter 'T' (20) + 4 = 24 ('X')
• The 1st letter 'S' (19) + 5 = 24 ('X')

Combining these letters in order gives: ZTRXX.