In each of the following numbers, replace M by the smallest number to make resulting number divisible by 11. (i) 39 M 2 (ii) 3 M 422

(i) 39 M 2

The given number = 39 M 2

Sum of its digits in odd places = 3 + M

Sum of its digits in even place = 9 + 2 = 11

Their Difference = 11 – (3 + M)

11 – (3 + M) = 0 

11 – 3 = M 

M = 8

(ii) 3 M 422

The given number = 3 M 422

Sum of its digits in odd places = 3 + 4 + 2 = 9

Sum of its digit in even places = M + 2

Difference of the two sums = 9 – (M + 2)

9 – (M + 2) = 0

9 – 2 = M

M = 7

(iii) 70975 M

The given number = 70975 M

Sum of its digits in odd places = 0 + 7 + M = 7 + M

Sum of its digit in even places = 5 + 9 + 7 = 21

Difference of the two sums = 21 – (7 + M)

=> 21 – (7 + M) = 0

=> 21 = 7 + M

=> M = 14

Since, M cannot be two digit number M = 14 – 11 = 3

(iv) 14 M 75

The given number = 14 M 75

Sum of its digit in odd places = 1 + M + 5 = M + 6

Sum of its digit in even places = 4 + 7 = 11

11 – (M + 16) = 0

11 = M + 6

11 – 6 = M

M = 5