The number ab - ba where a and b are digits and a > b is divisible by ________.

Solution:

If ab is written in the generalised form we get

ab = 10a + b

If ba is written in the generalised form we have

ba = 10b + a

Therefore

ab - ba = 10a + b - (10b + a) = 9a - 9b = 9(a - b)

Therefore the number ab - ba is divisible by 9.

✦ Try This: The number abc - cba where a and b are digits and a - b is divisible by ________.

If abc is written in generalised form we have:

abc = 100a + 10b + c - (100c + 10b + a) = 99a - 99c = 99(c - a)

Therefore abc - cba is divisible by 99

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16

NCERT Exemplar Class 8 Maths Chapter 13 Sample Problem 5

The number ab - ba where a and b are digits and a > b is divisible by ________.

Summary:

The number ab - ba where a and b are digits and a > b is divisible by 9.

☛ Related Questions:

• If AB × B = 9B, then A = _________, B = _________.
• If abc, cab, bca are three digit numbers formed by the digits a, b, and c then the sum of these numb . . . .
• Let ab be a two-digit number, then ab + ba is divisible by 9.