the sum of the digits of a 2 -digits number is 9.The new number obtained by interchanging the digits exceeds the given number by 27. find the given number
27
To find the given number, let's assume the tens digit is represented by variable 'x' and the units digit is represented by variable 'y'.
According to the given information, the sum of the digits of the 2-digit number is 9. This can be expressed as:
x + y = 9 --------(1)
The new number obtained by interchanging the digits exceeds the given number by 27. In other words, the new number is 27 more than 10y + x. This can be expressed as:
10y + x + 27 = 10x + y --------(2)
Now, let's solve the system of equations (1) and (2) to find the values of x and y.
From equation (1), we can rearrange it to express x in terms of y:
x = 9 - y
Substitute this value of x in equation (2):
10y + (9 - y) + 27 = 10(9 - y) + y
Simplifying the equation:
10y + 9 - y + 27 = 90 - 10y + y
Combine like terms:
9y + 36 = 90 - 9y
Bring all y terms to one side and constant terms to the other side:
18y = 90 - 36
Simplifying:
18y = 54
Divide both sides by 18:
y = 3
Now substitute the value of y back into equation (1):
x + 3 = 9
Subtract 3 from both sides:
x = 6
Therefore, the given number is 63.