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Question

# The digits of a two digit number differ by 7. If the digits are interchanged and the resulting numbers is added to original numbers, we get 121. What is the original number?

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Solution

## Given x and y be the required two digit number.Let the digit in ten's place be x.Let the digit in one's place be y.Therefore the required number is 10x+y. ------ (*)Given that the digits of a two digit number differ by 7.x - y = 7 ----- (1)Given that if the digits are interchanged and the resulting number is added to the original number we get 121.10x + y + 10y + x = 12111x + 11y = 121x + y = 11 -------------- (2).On solving (1) & (2), we getx + y = 11x - y = 7--------------2x = 18x = 9Substitute x = 9 in (1), we getx + y = 119 + y = 11y = 11 - 9y = 2.Substitute x & y in (*), we getThe original number = 10(9) + 2 = 90 + 2 = 92.

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