The equation given is ABC × D = 37DD, where A, B, C, and D are different non-zero digits.

Therefore,

ABC  = 37DD / D  

= (3700 + 10D + D) / D

= (3700 + 11D) / D

= (3700/D) + 11.

Given, ABC is a 3-digit number, i.e. it is an integer.

Hence, (3700/D) should also be an integer, means, it should be perfectly divisible.

Let’s check divisibility of 3700 from 1 to 9, D ≠ 3, 6, 7, 8, 9.

The possible values of D are 1, 2, 4, and 5.

•   If D = 1, ABC = (3700/1) + 11 = 3700 + 11 = 3711, which is not a three-digit number.

•   If D = 2, ABC = (3700/2) + 11 = 1850 + 11 = 1861, which is not a three-digit number.

•   If D = 5, ABC = (3700/5) + 11 = 740 + 11 = 751, but this is rejected because B = D = 5.

•   If D = 4, ABC = (3700/4) + 11 = 925 + 11 = 936.

Therefore, A + B + C = 9 + 3 + 6 = 18. 

Thus, option (a) is the correct answer.