A number consists of two digits.THe digit in tens place is twice that in units place.if 18 is subtracted from the number. The digits are reversed.find the number.

Let's express the number in terms of its digits. Let the digit in the tens place be x and the digit in the units place be y.

According to the given information, the digit in the tens place is twice that in the units place, so we have the equation:

x = 2y

We are also told that if 18 is subtracted from the number, the digits are reversed. This means that the new number is formed by switching the digits, so the new number is yx. We can represent this algebraically as:

10y + x - 18 = yx

We can substitute the value of x from the first equation into the second equation:

10y + 2y - 18 = y(2y)
12y - 18 = 2y^2

By rearranging the equation, we get:

2y^2 - 12y + 18 = 0

To solve this quadratic equation, we can factor out a common factor of 2:

2(y^2 - 6y + 9) = 0

Now, we can factor the quadratic expression inside the parentheses:

2(y - 3)^2 = 0

Setting each factor equal to zero, we find that:

y - 3 = 0

y = 3

Substituting this value back into the first equation, we can find the value of x:

x = 2y
x = 2(3)
x = 6

Therefore, the number is 63.

To find the number, we'll follow these steps:

Step 1: Assign variables
Let's assign variables to the digit in the tens place and the digit in the units place. Let's call the digit in the tens place "x" and the digit in the units place "y".

Step 2: Identify the given information
We know that the digit in the tens place is twice that in the units place. So, we can write the equation: x = 2y.

We also know that when 18 is subtracted from the number, the digits are reversed. This means that the original number can be written as 10x + y, and the number with the reversed digits can be written as 10y + x. So, we have the equation: 10x + y - 18 = 10y + x.

Step 3: Solve the equations
Let's solve the equations we have to find the values of x and y.

From equation 1 (x = 2y), we can substitute the value of x in equation 2:
10(2y) + y - 18 = 10y + 2y
20y + y - 18 = 10y + 2y
21y - 18 = 12y
21y - 12y = 18
9y = 18
y = 2

Now that we have the value of y, we can substitute it back into equation 1 to find the value of x:
x = 2y
x = 2(2)
x = 4

Step 4: Find the number
To find the original number, we can substitute the values of x and y into the expression 10x + y:
Number = 10x + y
Number = 10(4) + 2
Number = 40 + 2
Number = 42

Therefore, the number is 42.

If the number is ab, then

a = 2b
10a+b - 18 = 10b+a

42