Question:
sum of digits the of a two-digits number is 9.when we interchange the digits, it is found that the resulting new number is greater then the original number by 27.what is the two-digit number
Answer:
Let the digit in the number is xy
So number is 10x + y
Given, sum of the digits of a two-digit number is 9
=> x + y = 9 ..........................1
Again
10y + x = 10x+ y +27
=> 10y + x - 10x - y = 27
=> 9y - 9x = 27
=> 9(y - x) = 27
=> y - x = 27/9
=> y - x = 3 ..................2
Add equation 1 and 2, we get
x + y + y - x = 9 + 3
=> 2y = 12
=> y = 12/2
=> y = 6
Now, from equation 1, we get
=> x + 6 = 9
=> x = 9 - 6
=> x = 3
So the required number is 36
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