Question

In each of the following numbers, replace * by smallest digit to make it divisible by 9 :
(1) 56 * 5
U
(ü) 31 42
(iii) 5702 *
(it) 357 * 46
(0) 587 * 1
(ui) * 2066​

Answer 1

Answer:

1. 5625
2. 31842
3. 57024
4. 357246
5. 58761
6. 42066

Step-by-step explanation:

Test of divisiblility for 9 : For a number to be divisible by 9, then the sum of all the digits of the number should be divisible by 9

(1) 56 * 5

sum of digits = 5+6+*+5 = 16+*

      => 16+* = 18 (nearest number to 16 which is divisible by 9)

      => * = 18-16

      => * = 2

      => the number is 5625

(ii) 31*42

sum of digits = 3+1+*+4+2 = 10+*

      => 10+* = 18 (nearest number to 10 which is divisible by 9)

      => * = 18-10

      => * = 8

      => the number is 31842

(iii) 5702 *

sum of digits = 5+7+0+2+* = 14+*

      => 14+* = 18 (nearest number to 14 which is divisible by 9)

      => * = 18-14

      => * = 4

      => the number is 57024

(iv) 357 * 46

sum of digits = 3+5+7+ * +4+6 = 25+*

      => 25+* = 27 (nearest number to 25 which is divisible by 9)

      => * = 27-25

      => * = 2

      => the number is 357246

(v) 587 * 1

sum of digits = 5+8+7+*+1 = 21+*

      => 21+* = 27 (nearest number to 21 which is divisible by 9)

      => * = 27-21

      => * = 6

      => the number is 58761

(vi) * 2066​

sum of digits = *+2+0+6+6 = 14+*

      => 14+* = 18 (nearest number to 14 which is divisible by 9)

      => * = 18-14

      => * = 4

      => the number is 42066