Final answer:
To find the number, we need to set up and solve equations based on the given conditions. The answer is obtained by solving the equations and finding the values of the digits that make up the number. Hence the correct answer is option A
Step-by-step explanation:
To solve this problem, we need to set up an equation based on the information provided. Let's call the two numbers 'ab' and 'ba', where 'a' and 'b' represent the digits. The first condition states that when these two numbers are added, the result is 165. So, we have the equation 'ab + ba = 165'.
The second condition states that the two numbers differ by three. If we subtract the smaller number from the larger number, the result should be three. So, we have the equation 'ba - ab = 3'.
Now, let's solve these equations simultaneously to find the values of 'a' and 'b'. Subtracting the first equation from the second equation gives us 'ba - ab - (ab + ba) = 3 - 165' which simplifies to '-2ab = -162'. Dividing both sides by -2 gives us 'ab = 81'.
Since 'ab' represents the tens and units digits of a number, we can conclude that 'a' is 8 and 'b' is 1. Therefore, the number is 81. Hence, the correct answer is A. 102.