A number consists of two digits whose sum is 8. If 18 is added to the number its digits get interchanged. The number is?a) 53b) 35c) 92d) 63

Let's assume the number consists of two digits. Let the tens digit be represented as x and the ones digit as y.

So, the number can be written as: Number = 10x + y

Given:

The sum of the digits is 8. This means: x + y = 8

If 18 is added to the number, the digits get interchanged. This gives us the equation: (10x + y) + 18 = 10y + x

Now, let's solve the system of equations step by step.

Step 1: Simplify the second equation.
(10x + y) + 18 = 10y + x
This simplifies to:
10x + y + 18 = 10y + x
Now, move all terms involving x and y to one side:
10x - x = 10y - y - 18
9x = 9y - 18
Divide both sides by 9:
x = y - 2

Step 2: Substitute into the first equation.
We know x + y = 8. Substitute x = y - 2 into this equation:
(y - 2) + y = 8
2y - 2 = 8
2y = 10
y = 5

Step 3: Find x.
Now that we know y = 5, substitute this value into the equation x = y - 2:
x = 5 - 2
x = 3

Step 4: Construct the number.
The tens digit is 3 and the ones digit is 5. So, the number is 35.

Thus, the number is 35.

Answer: b) 35