The difference of a two-digit number and the number obtained by reversing its digits is always divisible by ___________. Fill in the blank to make the statement true

Solution:

Let the two digit number be xy. The reverse is yx. If we write both the numbers in generalised form we have:

xy = 10x + y --- (1)

yx = 10y + x --- (2)

Subtracting (2) from (1) we get

xy + yx = 9x - 9y = 9(x - y)

Therefore we can state that the difference of a two digit number and its reverse is always divisible by 9.

✦ Try this: The difference of a three -digit number and the number obtained by reversing its digits is always divisible by ___________. Fill in the blank to make the statement true

Let the three digit number be xyz. The reverse is zyx. If we write both the numbers in generalised form we have:

xyz = 100x + 10y + z --- (1)

zyx = 100z + 10y + x --- (2)

Subtracting (2) from (1) we get

99x - 99z = 99(x - z)

Therefore the difference of a three -digit number and the number obtained by reversing its digits is always divisible by 99.

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

---

NCERT Exemplar Class 8 Maths Chapter 13 Problem 22

The difference of a two-digit number and the number obtained by reversing its digits is always divisible by ___________. Fill in the blank to make the statement true

Summary:

The difference of a two-digit number and the number obtained by reversing its digits is always divisible by 9.

---

☛ Related Questions:

• The difference of three-digit number and the number obtained by putting the digits in reverse order . . . .
• If 2 B + A B = 8 A, then A = ______ and B = ______. Fill in the blank to make the statement true
• If A B × B = 96, then A = ______ and B = ______. Fill in the blank to make the statement true