Selina solutions

# Question 11

Q11)In each of the following numbers, replace M by the smallest number to make resulting number divisible by 3 :

(i) 64 M 3

(ii) 46 M 46

(iii) 27 M 53

Solution :

(i) 64 M 3

The given number = 64 M 3

For a number to be divisible by 3 sum of digits must be divisible by 3.

Sum of its digits = 6 + 4 + 3 = 13

The number next to 13 which is divisible by 3 is 15

Required smallest number = 15 - 13 = 2

Therefore, value of M is 2.

(ii) 46 M 46

The given number = 46 M 46

For a number to be divisible by 3 sum of digits must be divisible by 3.

Sum of its digits = 4 + 6 + 4 + 6 = 20

The number next to 20 which is divisible by 3 is 21

Required smallest number = 21 - 20 = 1

Therefore, value of M is 1.

(iii) 27 M 53

The given number = 27 M 53

For a number to be divisible by 3 sum of digits must be divisible by 3.

Sum of its digits = 2 + 7 + 5 + 3 = 17

The number next to 17 which is divisible by 3 is 18

Required smallest number = 18-17=1

Therefore, value of M is 1.

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