The sum of a two-digit number and the number obtained by reversing the 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)

Adding (1) and (2) we get

xy + yx = 11x + 11y = 11(x + y)

Therefore we can state that the sum of a two digit number and its reverse is always divisible by 11.

✦ Try This: The sum of a three-digit numbers formed by the digits x, y and z is always divisible by __________.

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)

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

yzx = 100y + 10z + x ----- (3)

Adding (1) (2) and (3) we get

111x + 111y + 111z

111(x + y + z)

Therefore we can state that the sum of a three digit numbers made from digits x, y and z is always divisible by 111.

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

NCERT Exemplar Class 8 Maths Chapter 13 Problem 21

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

Summary:

The sum of a two digit number xy and its reverse yx is always divisible by 11.

☛ Related Questions: