Problem Statement:
The sum of the digits of a two-digit number is 10. If 18 is subtracted from it, the digits in the resulting number will be equal. Find the number.

Solution:

Step 1: Understand the problem
We are given a two-digit number whose digits sum up to 10. When we subtract 18 from this number, the resulting number has equal digits. We need to find the original number.

Step 2: Let's assume the two-digit number
Let's assume the two-digit number as 'xy', where x represents the tens digit and y represents the units digit. So, the original number can be represented as 10x + y.

Step 3: Write the given conditions as equations
From the problem statement, we have two conditions:
1. The sum of the digits is 10: x + y = 10
2. The resulting number after subtracting 18 has equal digits: (10x + y) - 18 = yy

Step 4: Solve the equations
We have two equations with two unknowns. We can solve them simultaneously to find the values of x and y.

From equation 1, we can express x in terms of y: x = 10 - y

Substituting this value of x in equation 2, we get: (10 - y) + y - 18 = yy
Simplifying the equation, we get: 10 - 18 = yy - y
-8 = y(y - 1)

Step 5: Find the possible values of y
To find the possible values of y, we can factorize -8 and check for the values of y that satisfy the equation -8 = y(y - 1).

-8 can be factorized as (-4)(2) or (-2)(4) or (1)(-8)

For (-4)(2), we have:
y = -4, y - 1 = 2
y = 4, y - 1 = -2

For (-2)(4), we have:
y = -2, y - 1 = 4
y = 3, y - 1 = -4

For (1)(-8), we have:
y = 1, y - 1 = -8
y = 9, y - 1 = 0

Step 6: Check the valid values of y
Out of the possible values of y, we need to check which values satisfy the condition x + y = 10.

For y = 4, we have x = 10 - 4 = 6
For y = 3, we have x = 10 - 3 = 7
For y = 1, we have x = 10 - 1 = 9

Step 7: Final answer
From the above calculations, we find that the possible two-digit numbers satisfying the given conditions are 64, 73, and 91.

Therefore, the number can be 64 or 73 or 91.

It would've been easier with the options..because..u can try the given information on the option_
anyways
x+y=10
73 -18=55
and 7+3=10(by trial and error method...)