If number a is a 2-digit number and its digits are transposed to form number b, then the difference between the larger of the two numbers and the smaller of the two numbers must be divisible by

a.8
b.7
c.9
d. an even number

The required numbers must be divisible by 9 .

Given that,

Number A is 2 digit number and its digits are transposed to form number B,

We have to find,

The difference between the larger of the two numbers and the smaller of the two numbers must be divisible by.

According to the question,

The 2 digit number is ab it has a value of

Larger of the two number = 10a+b

When it is reversed it will have a value of

Smaller of the two numbers = 10b-a ,

The difference between the larger of the two numbers and the smaller of the two numbers,

= 10a + b - 10b - a

= 9a - 9b

Divided by 9

= a - b

So, The numbers must be divisible by 9.

Hence, The required numbers must be divisible by 9 .

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