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Question

The sum of a two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there?

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Solution

Let the two-digit be x and y .
Two-digit number =10x+y.
Two-digit number formed by interchanging the digits=10y+x
(10x+y)+(10y+x)=66x+y=6(i)
11x+11y=66xy=2(ii)
Substracting (i) and (ii),
2x=8
x=4
putting x in (i),
4+y=6
y=2
Two-digit number=10x+y=42 or, 10y+x=24
2 such numbers are possible.

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