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1. A number consists of two digits. If the digits interchange place and the new number is added to the original number, then the resulting number will be divisible by :
Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x
∴ (10x + y) + (10y + x)
= 11(x + y), which is divisible by 11
Solution:
Let the ten's digit be x and unit's digit be yThen, number = 10x + y
Number obtained by interchanging the digits = 10y + x
∴ (10x + y) + (10y + x)
= 11(x + y), which is divisible by 11