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If abc, bca and cab are three digit numbers, and

abc + bca + cab = 3 × (a + b + c) × k, then the value of k will be:


1. 33
2. 37
3. 111
4. 11

1 Answer

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Best answer
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

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