Q9 of 186 Page 4

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

Let unit’s digit = y

and the ten’s digit = x


So, the original number = 10x + y


The sum of the number = 10x + y


The sum of the digit = x + y


reversing number = x + 10y


According to the question,


10x + y + x + 10y = 66


⇒11x + 11y = 66


⇒ x + y = 6 …(i)


x – y = 2 …(ii)


By cross - multiplication method, we have





On taking I and III ratio, we get



⇒ x = 4


On taking II and III ratio, we get



⇒ y = 2


So, the original number = 10x + y


= 10(4) + 2


= 42


Reversing the number = x + 10y


= 24


Hence, the two digit number is 42 and 24. These are two such numbers.


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