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प्रश्न
The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.
उत्तर
Let x be the unit's digit and y the tens digit.
∴ Two digit number = 10y + x
Number obtained on interchanging the digits = 10x + y.
The sum of a two digit number and the number obtained by interchanging its digits is 99.
10x + y + 10y + x = 99
⇒ 11x + 11y = 99
Divide both sides by 11
⇒ x + y = 9
If x = 1, then y = 8,
If x = 2, then y = 7, etc.
With the given information, only one equation can be formed.
So, the number can be 81, 72, 63, 54.
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