Correct Answer - Option 2 : 37
Concept used:
Any number can be written as digit × place value
For example:- 354 = 3 × 100 + 5 × 10 + 4 × 1 = 300 + 50 + 4
Solution:
abc + bca + cab = 3 × (a + b + c) × k
⇒ (100a + 10b + c) + (100b + 10c + a) + (100c + 10a + b) = 3 × (a + b + c) × k
⇒ (100a + 10 a + a) + (100b + 10b + b) + (100c + 10c + c) = 3 × (a + b + c) × k
⇒ 111a + 111b + 111c = 3 × (a + b + c) × k
⇒ 111 × (a + b + c) = 3 × (a + b + c) × k
⇒ k = 111/3
⇒ k = 37