✅ In this position-value coding, each letter is assigned its numerical position in the alphabet (A=1, B=2, ..., Z=26).

The given example `APPLE` (A=1, P=16, P=16, L=12, E=5) coded as `2-16-16-13-6` reveals a specific pattern of modification based on the letter's position within the word.

The pattern is: the 1st, 4th, and 5th letters' position values are increased by 1, while the 2nd and 3rd letters' position values remain unchanged.

Applying this pattern to `GRAPE` (G=7, R=18, A=1, P=16, E=5): G (1st) becomes 7+1=8, R (2nd) remains 18, A (3rd) remains 1, P (4th) becomes 16+1=17, and E (5th) becomes 5+1=6.

Therefore, `GRAPE` is coded as `8-18-1-17-6`.

❌ Options B, C, and D do not follow this specific word-position based coding pattern, either showing direct position values, adding 1 to all, or other incorrect transformations.

✅ The coding rule involves two steps: first, find the alphabetical position value for each letter (A=1, B=2, ..., Z=26). Second, sum the digits of each position value, and then sum these individual digit-sums for all letters in the word.

For "PEN":

• P has position 16 → 1 + 6 = 7
• E has position 5 → 5
• N has position 14 → 1 + 4 = 5

Total code for PEN = 7 + 5 + 5 = 17.

For "TOP":

• T has position 20 → 2 + 0 = 2
• O has position 15 → 1 + 5 = 6
• P has position 16 → 1 + 6 = 7

Total code for TOP = 2 + 6 + 7 = 15.

Applying this rule to "MAP":

• M has position 13 → 1 + 3 = 4
• A has position 1 → 1
• P has position 16 → 1 + 6 = 7

Total code for MAP = 4 + 1 + 7 = 12.

❌ This option would be correct if the code was simply the direct sum of the letters' alphabetical position values (M=13, A=1, P=16; 13+1+16=30), which is not the established pattern.

❌ This option does not align with the established pattern or calculation method derived from the examples.

❌ This option does not align with the established pattern or calculation method derived from the examples.

✅ In this position-value coding system, each letter of a word is replaced by its corresponding alphabetical position value (A=1, B=2, ..., Z=26), and these numerical values are then concatenated. For 'APPLE', the values are A=1, P=16, P=16, L=12, E=5, which concatenate to '11616125'. Applying this rule to 'MANGO': M=13, A=1, N=14, G=7, O=15. Concatenating these values (13, 1, 14, 7, 15) results in '13114715'.

❌ Option B is incorrect as it omits the '1' for the letter 'A'.

❌ Option C is incorrect as it omits the '1' for 'A' and incorrectly uses '5' instead of '15' for 'O'.

❌ Option D is incorrect due to an extra '1' or misplaced '1' digit, leading to an incorrect sequence.

✅ The coding rule involves two steps: first, sum the alphabetical position values of all letters in the word (A=1, B=2, ..., Z=26); second, multiply this sum by the total number of letters in the word.

For 'RING': R(18) + I(9) + N(14) + G(7) = 48. The word 'RING' has 4 letters. So, 48 × 4 = 192.

For 'CODE': C(3) + O(15) + D(4) + E(5) = 27. The word 'CODE' has 4 letters. So, 27 × 4 = 108.

Applying this rule to 'VERBAL': V(22) + E(5) + R(18) + B(2) + A(1) + L(12) = 60.

The word 'VERBAL' has 6 letters. Therefore, 60 × 6 = 360.

❌ Option B (300) would be incorrect as it might result from summing the position values and multiplying by 5 (60 * 5), which doesn't follow the established pattern.

❌ Option C (240) would be incorrect, potentially derived from summing the position values and multiplying by 4 (60 * 4), which is not the number of letters in 'VERBAL'.

❌ Option D (420) would be incorrect as it might result from summing the position values and multiplying by 7 (60 * 7), which is an arbitrary multiplier.

✅ First, determine the coding rule by analyzing the given examples using numerical position values (A=1, B=2, ..., Z=26).

For "CAT": The sum of position values is C(3) + A(1) + T(20) = 24. The word "CAT" has 1 vowel (A). So, 24 × 1 = 24.

For "DOG": The sum of position values is D(4) + O(15) + G(7) = 26. The word "DOG" has 1 vowel (O). So, 26 × 1 = 26.

The established rule is: calculate the sum of the numerical position values of the letters, then multiply this sum by the total number of vowels in the word.

Applying this rule to "TRAIN": The sum of position values is T(20) + R(18) + A(1) + I(9) + N(14) = 62.

The word "TRAIN" has 2 vowels (A and I). Therefore, 62 × 2 = 124.

❌ Option A (62) is incorrect because it represents only the sum of the position values, without applying the multiplier based on the number of vowels.

❌ Option C (186) is incorrect; this would be the sum of position values multiplied by the number of consonants (62 × 3), which does not follow the established coding pattern.

❌ Option D (310) is incorrect; this would be the sum of position values multiplied by the total number of letters in the word (62 × 5), which is not consistent with the given examples.