sum of digits o two digit no is 7 . if digits are interchanged the number formed is greater than original by 27
Answers
Let the units digit be x and the tens digit be y.
Therefore, the number is 10y + x.
According to the first condition,
x + y = 7 -------(1)
According to the second condition,
10x + y = 10y + x + 27
10x - x + y - 10y = 27
9x - 9y = 27
x - y = 3 ------(2) ----Divided by 9
Add equations (1) and (2), we get
x + y + x - y = 7 + 3
2x = 10
x = 10/2
x = 5
Substitute x = 5 in equation (2), we get
5 - y = 3
- y = 3 - 5
- y = - 2
y = 2
Substitute x=5 and y=2 in the equation 10y + x, we get
10(2) + 5 = 20 + 5 = 25.
Hence the number is 25.
Let the tens digit be x and the units digit be y.
Therefore, the number is 10x + y.
According to the first condition,
x + y = 7 -------(1)
According to the second condition,
10x + y + 27 = 10y + x
10x - x + y - 10y = - 27
9x - 9y = - 27
x - y = - 3 ------(2) ----Divided by 9
Add equations (1) and (2), we get
x + y + x - y = 7 - 3
2x = 4
x = 4/2
x = 2
Substitute x = 2 in equation (2), we get
2 - y = - 3
y = 2 + 3
y = 5
Substitute x= 2and y=5 in the equation 10x + y, we get
10(2) + 5 = 20 + 5 = 25.
Hence the number is 25.
