Find the value of $$K^2$$​ − 3K, for which the number 58K764 is divisible by 11.

Correct option is A

Given:​

​58K764 is divisible by 11 

Concept Used: ​

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is divisible by 11:

(Sum of odd-position digits) − (Sum of even-position digits) = 0 or divisible by 11

Solution: 

58K764 

Sum of odd Position number = 4 + 7 + 8 = 19 

Sum of even position number = 5 + K + 6 = 11 + k 

Sum of odd place - Sum of even place = 0 

19 - ( 11 + K ) = 0 

K = 8 

So, 

​$$K^2 - 3K \\ \ \\ = 8^2 - 3 \times 8 \\ \ \\ = 40$$​​