In a certain code language, if CABINET = 70 and BEAUTY = 60, then PRODUCTION = ?

If CABINET = 70 and BEAUTY = 60, then the code is likely derived from some transformation of the letters in the word into numbers.

Step-by-step analysis:

1. Assign the positional value of letters in the alphabet:
   • A = 1, B = 2, ..., Z = 26.

2. Compute the sum of letter values in each word:

   • CABINET:
     • C = 3, A = 1, B = 2, I = 9, N = 14, E = 5, T = 20
     • Sum = 3 + 1 + 2 + 9 + 14 + 5 + 20 = 54.
     • To get 70, add a constant: 54+16=7054 + 16 = 7054+16=70.
   • BEAUTY:
     • B = 2, E = 5, A = 1, U = 21, T = 20, Y = 25
     • Sum = 2 + 5 + 1 + 21 + 20 + 25 = 74.
     • To get 60, subtract a constant: 74−14=6074 - 14 = 6074−14=60.

   This suggests a pattern where a specific constant is added or subtracted to/from the sum of letter values.

3. Test this on PRODUCTION:
   • PRODUCTION:
     • P = 16, R = 18, O = 15, D = 4, U = 21, C = 3, T = 20, I = 9, O = 15, N = 14
     • Sum = 16+18+15+4+21+3+20+9+15+14=13516 + 18 + 15 + 4 + 21 + 3 + 20 + 9 + 15 + 14 = 13516+18+15+4+21+3+20+9+15+14=135.
     • To achieve 100, subtract 35: 135−35=100135 - 35 = 100135−35=100.

Thus, the logic is:

1. Calculate the sum of positional values of letters.
2. Subtract a constant (specific to the word): 353535 for "PRODUCTION."

Final answer: 100