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Question

The sum of a two digit number and the number obtained by reversing the order of the digits is 165 if the digits differ by 3 find the number


Solution

Let 1 digit be y.

:. Other digit will be y - 3

So, the no. is 10y + y - 3 = 11y-3

By reversing the digits the no. becomes 10(y - 3) + y = 11y - 30.

Sum of the 2 nos. = 165

11y - 3 + 11y - 30 = 165

22y - 33 = 165

22y = 198

y = 9

So, the no. is 96.

Since the digits differ by 3, they could be y and y +3.

So, the no. becomes 10y + y + 3 = 11y + 3

By reversing the digits, it becomes 10(y + 3) + y = 11y + 30

Therefore, 11y + 3 + 11y +30 = 165

22y +33 = 165

22y = 132

y = 6

Therefore the no. is 69

So the number is 69 or 96

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