Sum of the digits of a two-digit number is 9. When we interchange that digit , it is found that the resulting new number is greater than the original number by 27. What is the two digit number?
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Answered by
11
let the 2 digits at ten's place be x and at one's palce be y.
then the original no. will be 10x+y
and x+y = 9 .........(i)
the no. obtained by interchanging the digits will be 10y+x
ATQ, (10y+x) - (10x+y) =27
10y+x - 10x -y = 27
9y-9x= 27
-x + y = 3............(ii)
by adding (i) and (ii) , we get-
y= 6
and putting this value in (i), we get,
x=3
Therefore, the original no. is= 10×3 +6= 36
Hope it helps you bro
Took a lot time to type
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then the original no. will be 10x+y
and x+y = 9 .........(i)
the no. obtained by interchanging the digits will be 10y+x
ATQ, (10y+x) - (10x+y) =27
10y+x - 10x -y = 27
9y-9x= 27
-x + y = 3............(ii)
by adding (i) and (ii) , we get-
y= 6
and putting this value in (i), we get,
x=3
Therefore, the original no. is= 10×3 +6= 36
Hope it helps you bro
Took a lot time to type
plz mark brainliest if you liked
Answered by
0
Answer:
Given
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
Hence the number is 36
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