Question

A two-digit positive number is such that the ones digit is 2.5 times as much as the tens digit. If the difference between the number and the number obtained when the digits are reversed is 27, find the number.

a) 25
b) 37
c) 48
d) 61

Answer 1

a) 25

Step-by-step explanation:

Trial and error shows that only A can be the answer.

The ones digit is 5 and the tens digit is 2. 2 * 2.5 is 5, but just to make sure, we can confirm the second part.

25 with the digits reversed is 52, so it would be 52 - 25

This gives 27 like the question asks.

Answer 2

To find the number, set up an equation using the given information and solve for the tens digit. The ones digit is 2.5 times the tens digit. The number obtained when the digits are reversed is 27 less than the original number. The solution is x = 2, giving a number of 25.

Step-by-step explanation:

To find the number, we can set up an equation using the given information:

Let the tens digit be x.

The ones digit is 2.5 times the tens digit, so it is 2.5x.

The original number can be expressed as 10x + 2.5x = 12.5x.

The number obtained when the digits are reversed is 10(2.5x) + x = 25x + x = 26x.

The difference between the original number and the reversed number is 12.5x - 26x = -13.5x.

Given that the difference is 27, we can solve the equation:

-13.5x = 27

x = -27/-13.5 = 2

The tens digit is 2, and the ones digit is 2.5 times the tens digit, which is 2.5 * 2 = 5.

Therefore, the number is 25.