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Question
Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.
Solution
Let the unit’s digit be x.
Then, the ten’s digit = 11 – x
∴ Number = 10(11 – x) + x
= 110 – 10x + x
= 110 – 9x
Number obtained by interchanging the digits
= 10x + (11 – x)
= 9x + 11
According to the question,
9x + 11 – (110 – 9x) = 9
⇒ 9x + 11 – 110 + 9x = 9
⇒ 18x = 9 – 11 + 110
⇒ 18x = 108
⇒ x = `108/18`
⇒ x = 6
Hence, unit’s digit = 6 and ten’s digit = 11 – 6 = 5
Therefore, the required number is 56.
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