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प्रश्न
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.
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उत्तर
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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