some of the sum of the digits of a two-digit number is 9 when we interchange the digits it is found that the resulting new number is greater than the original number by 27what is the two digit number
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The sum of the two digits = 9
On interchanging the digits, the resulting new number is greater than the original number by 27.
Let us assume the digit of units place = x
Then the digit of tens place will be = (9 – x)
Thus the two-digit number is 10(9 – x) + x
Let us reverse the digit
the number becomes 10x + (9 – x)
As per the given condition
10x + (9 – x) = 10(9 – x) + x + 27
⇒ 9x + 9 = 90 – 10x + x + 27
⇒ 9x + 9 = 117 – 9x
On rearranging the terms we get,
⇒ 18x = 108
⇒ x = 6
So the digit in units place = 6
Digit in tens place is
⇒ 9 – x
⇒ 9 – 6
⇒ 3
Step-by-step explanation:
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