NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Exercise 16.2

Ques: If A and B play a game with numbers and A asks B to choose a two-digit number first. Then, A asks B to reverse the digits of the number and add them up. A then says to divide the number so obtained by 11. A guarantees B that there will be no remainder. Reason out.

Soln:

Let the number chosen by B = ab

Then, reversing the number B gets, ba

Condition given is,

ab + ba = 11(a + b)

(ab+ba) should be completely divisible by (a+b) and 11. 

Thus there will be no remainder when (ab+ba) is divisible by 11.