Question

The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.

A.43
B.61
C.52
D.25

Answer 1

To find the original number, set up a system of equations based on the given information. Solve the system to find that the original number is 43.Option A is the correct answer.

Step-by-step explanation:

To find the original number, we can set up a system of equations based on the given information. Let's assume the tens digit is 'x' and the ones digit is 'y'. Given that the sum of the digits is 7, we have the equation x + y = 7.

The number formed by interchanging the digits can be expressed as 10y + x. We are told that this number is less than the original number by 27, so we have the equation 10y + x = (10x + y) - 27.

Solving this system of equations, we find that x = 4 and y = 3. Therefore, the original number is 43, so the answer is A.43.