In a code language, ‘GOOD’ is written as ‘HMPB’, and ‘HALL’ is written as ‘IYMJ’. How will ‘TOOL’ be written in that language?

The correct option is UMPJ.

Let us analyze the pattern used in the code language by comparing the letters of the original words with their coded counterparts. We will look at the position of each letter in the standard English alphabet:

A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, Q = 17, R = 18, S = 19, T = 20, U = 21, V = 22, W = 23, X = 24, Y = 25, Z = 26

First Example: 'GOOD' is coded as 'HMPB'
Let us examine the transition for each letter position:
1st letter: G → H (G is 7th, H is 8th. Change: +1)
2nd letter: O → M (O is 15th, M is 13th. Change: -2)
3rd letter: O → P (O is 15th, P is 16th. Change: +1)
4th letter: D → B (D is 4th, B is 2nd. Change: -2)
Thus, the shift pattern is alternately +1 and -2.

Second Example: 'HALL' is coded as 'IYMJ'
Let us verify the shift pattern using 'HALL':
1st letter: H → I (H is 8th, I is 9th. Change: +1)
2nd letter: A → Y (A is 1st. Moving backward 2 positions: A → Z → Y. Change: -2)
3rd letter: L → M (L is 12th, M is 13th. Change: +1)
4th letter: L → J (L is 12th, J is 10th. Change: -2)
The pattern (+1, -2, +1, -2) is consistent.

Applying the pattern to 'TOOL':
1st letter: T + 1 = U (T is 20th, 20 + 1 = 21, which is U)
2nd letter: O - 2 = M (O is 15th, 15 - 2 = 13, which is M)
3rd letter: O + 1 = P (O is 15th, 15 + 1 = 16, which is P)
4th letter: L - 2 = J (L is 12th, 12 - 2 = 10, which is J)

Putting the coded letters together, 'TOOL' is written as UMPJ.