In a certain code language, ‘BUZZY’ is coded as ‘10’ and ‘KING’ is coded as ‘8’. How will ‘ABROAD’ be coded in that language?

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Step 1: Analyze the given codes.
- BUZZY is coded as 10
- KING is coded as 8

Step 2: Assign numerical values to letters based on their position in the alphabet:
B=2, U=21, Z=26, Y=25, K=11, I=9, N=14, G=7

Step 3: Check the sum of the letters for BUZZY:
B(2) + U(21) + Z(26) + Z(26) + Y(25) = 2 + 21 + 26 + 26 + 25 = 100

Step 4: Check the sum of the letters for KING:
K(11) + I(9) + N(14) + G(7) = 11 + 9 + 14 + 7 = 41

Step 5: The code given is much smaller than the sum, so check the number of letters:
BUZZY has 5 letters, KING has 4 letters.

Step 6: Check if the code corresponds to the number of letters or something else:
BUZZY code = 10, KING code = 8

Step 7: Try sum of digits of the sum:
BUZZY sum = 100, sum of digits = 1 + 0 + 0 = 1 (does not match 10)
KING sum = 41, sum of digits = 4 + 1 = 5 (does not match 8)

Step 8: Try sum of positions of letters divided by number of letters:
BUZZY: 100 / 5 = 20 (not 10)
KING: 41 / 4 = 10.25 (not 8)

Step 9: Try counting the number of letters with vowels or consonants:
BUZZY vowels: U, Y (Y considered vowel here) = 2
KING vowels: I = 1

Step 10: Try counting number of letters with even positions:
BUZZY letters: B(2), U(21), Z(26), Z(26), Y(25)
Even position letters: B(2), Z(26), Z(26) = 3 letters
Sum of even position letters: 2 + 26 + 26 = 54

KING letters: K(11), I(9), N(14), G(7)
Even position letters: N(14) only
Sum = 14

Step 11: Try counting number of letters with odd positions:
BUZZY odd position letters: U(21), Y(25) = 2 letters
KING odd position letters: K(11), I(9), G(7) = 3 letters

Step 12: Try sum of letters minus number of letters:
BUZZY: 100 - 5 = 95 (not 10)
KING: 41 - 4 = 37 (not 8)

Step 13: Try sum of letters divided by 10:
BUZZY: 100 / 10 = 10 (matches code)
KING: 41 / 10 = 4.1 (not 8)

Step 14: Try sum of letters divided by 5:
BUZZY: 100 / 5 = 20 (not 10)
KING: 41 / 5 = 8.2 (close to 8)

Step 15: Try sum of letters divided by number of letters rounded:
BUZZY: 100 / 5 = 20 (not 10)
KING: 41 / 4 = 10.25 (not 8)

Step 16: Try sum of letters divided by 10 and then subtract number of letters:
BUZZY: (100 / 10) - 5 = 10 - 5 = 5 (not 10)
KING: (41 / 10) - 4 = 4.1 - 4 = 0.1 (not 8)

Step 17: Try sum of letters divided by 5 and subtract 10:
BUZZY: (100 / 5) - 10 = 20 - 10 = 10 (matches code)
KING: (41 / 4) - 10 = 10.25 - 10 = 0.25 (not 8)

Step 18: Since no clear pattern emerges, try counting number of letters in the word:
BUZZY has 5 letters, code is 10 (double the letters)
KING has 4 letters, code is 8 (double the letters)

Step 19: So code = 2 × number of letters

Step 20: ABROAD has 6 letters
Code = 2 × 6 = 12

Step 21: Check options, 12 is option 4

Therefore, the code for ABROAD is 12.

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