The difference between a two-digit number and the number obtained by i

Explanation

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let ten's and unit's digits be 2x and x respectively.

Then, (10 x 2x + x) - (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) - (2x - x) = 2x = 8.

Your point is valid. Ratio comes out to be 2:1. Though question above has the same wordings as written in the official source, I make the necessary change.

difference between digits=36/9=4
if ratio is 2:1, digits must be 8 and 4
(8+4)-(8-4)=8
B

It's written that the ratio between the numbers is 2:1.

So the only two-digit numbers that could be are:

x y

2 1
4 2
6 3
8 4

\(84-48 = 36\)

So \(8 + 4 = 12\) and \(8 - 4 = 4\)

\(12 - 4 = 8\)

B

Solution:

Let’s say we randomly pick a two-digit number (with tens digit > units digit), e.g., 51. Reversing the tens and units digits, we have 15 and 51 - 15 = 36. So we have a difference of 36, however, the ratio between the digits is not 1 : 2.

Let’s pick another two-digit number, say 72. Reversing the tens and units digits, we have 27 and 72 - 27 = 45. This time, we have neither a difference of 36 nor a ratio of 1 : 2. However, not all is lost.

Notice that 51 - 15 = 36 = 4 x 9 and 72 - 27 = 45 = 5 x 9. We see that in the first example, the difference between the units and tens digits is 4, the difference between the two numbers is 4 x 9, and in the second example, the difference between the units and tens digits is 5, the difference between the two numbers is 5 x 9. Since we want the difference of the two numbers to be 36, which is 4 x 9, we want the difference between the units and tens digits to be 4. Since we also want the ratio between the digits of the number to 1 : 2, we can see that the units digit must be 4 and the tens digit must be 8. In other words, the number and its digit-reversing counterpart are 84 and 48 (notice that 84 - 48 = 36). So we have the sum of the digits = 8 + 4 = 12 and the difference of the digits = 8 - 4 = 4 and the difference between the sum of the digits and the difference of the digits is 12 - 4 = 8.

Alternate Solution:

Since the ratio between the two digits is 1:2, the number can be 12, 24, 36 or 48. Reversing the digits and subtracting the original number from it, we get: 21 - 12 = 9; 42 - 24 = 18; 63 - 36 = 27 and 84 - 48 = 36. Thus, the number we are looking for is 48; the sum of the digits is 4 + 8 = 12 and the difference of the digits is 8 - 4 = 4. Thus, the difference between the two is 12 - 4 = 8.

Answer: B