Q. 113.9( 21 Votes )
The sum of the digits of a two - digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
Let the two - digit number be xy (i.e. 10x + y).
After interchanging the digits of the number xy, the new number becomes yx (i.e. 10y + x).
According to question -sum of the digits is 12
⇒ x + y = 12.....(1)
Also, the number obtained by interchanging its digits exceeds the given number by 18
⇒ (10y + x) - (10x + y) = 18
⇒ - 9x + 9y = 18
⇒ - x + y = 2.....(2)
Adding equations (1) and (2), we get -
x + y - x + y = 10 + 4
⇒ 2y = 14
⇒ y = 7
Substitute the value of y in equation (1), we get -
x = 5
Thus, the required number is 57.
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