Question

find the two digits a and b such that the 5 digit number 19 a 9 b is divisible by 36

Answer 1

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In this question we have to find the value of a and b in number 19 a 9 b that is completely divisible by 36.

= ( 19 a 9 b ) ÷ 36

= ( 19 a 9 b ) ÷ ( 9 × 4 )

We know that for any number to be divisible by 4 , its last 2- digit should be divisible by 4.

Now,

= ( 9 b ) ÷ 4

The possible values of b can be 2 or 6.

Now, for any number to be divisible by 9, the sum of all digits of number should be divisible by 9.

= ( 19 a 9 b ) ÷ 9

= ( 28 + a + b ) ÷ 9

If b = 2.

= ( 28 + a + 2 ) ÷ 9

= ( 30 + a ) ÷ 9

The possible value of a is 6.

If,b = 6.

= ( 19 a 9 b ) ÷ 9

= ( 28 + 6 + a ) ÷ 9

= ( 34 + a ) ÷ 9

So, possible value of a is 2.

The final answer is [ a = 2, b = 6 ] and [ a = 6 , b = 2 ].


Hope it helps !!