Which of the following is true about the absolute difference between a two- digit number and the number obtained by reversing its digits?a)It is divisible by 11.b)It is divisible by 6.c)It is divisible by 9.d)It is divisible by 7.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Let the units digit and tens digit be 'a' and 'b' respectively.

The number = 10b + a

Required difference = |(10b + a) - (10a +b)|= |9b - 9a| = 9 x |b - a|

The difference will always be divisible by 9.
Hence, option 3.

Answer

It can be understood by taking any arbitrary 2 digit no .

Answer

It is always divisible by 9
eg
29 and 92
|29-92|=63
|10-01|=9

Answer

It is always divisible by 9 for eg 83 [83-38]= 45 divisible by 9  and 42 [42-24] =18 divisible by 9

Answer

Let the units digit and tens digit be 'a' and 'b' respectively.

The number = 10b + a

Required difference = |(10b + a) - (10a +b)|= |9b - 9a| = 9 x |b - a|

The difference will always be divisible by 9.
Hence, option 3.

Answer

If I reverse 9 then its become absolute difference between a two- digit number. right ?

Answer

The absolute difference between a two-digit number and the number obtained by reversing its digits can be found by subtracting the two numbers. Let's consider a two-digit number AB, where A represents the tens digit and B represents the units digit.

To reverse the digits, we obtain the number BA. The absolute difference between AB and BA can be calculated as follows:

AB - BA = 10A + B - (10B + A) = 9A - 9B = 9(A - B)

From this expression, we can see that the absolute difference is always divisible by 9, regardless of the values of A and B. This means that option c) is true.

Explanation:

To understand why the absolute difference is always divisible by 9, let's consider a few examples:

1) If we take the number 23, its reverse is 32. The absolute difference is 23 - 32 = -9, which is divisible by 9.

2) If we take the number 78, its reverse is 87. The absolute difference is 78 - 87 = -9, which is again divisible by 9.

3) If we take the number 36, its reverse is 63. The absolute difference is 36 - 63 = -27, which is divisible by 9.

We can observe that the absolute difference is always a multiple of 9. This is because when we subtract the two numbers, we are effectively subtracting the sum of their digits. The difference will always be a multiple of 9 because the digits vary by a multiple of 9. For example, in the number 23, the difference between the tens digit (2) and the units digit (3) is 1, which is a multiple of 9.

In conclusion, the absolute difference between a two-digit number and the number obtained by reversing its digits is always divisible by 9.

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