The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? Options : none 4 8 6
Question
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options : none 4 8 6
Solution
Let's denote the tens digit as x and the units digit as y.
Given that the ratio of the digits is 1:2, we can write y = 2x.
The two-digit number is 10x + y and the number obtained by interchanging the digits is 10y + x.
According to the problem, the difference between these two numbers is 36:
10x + y - (10y + x) = 36 9x - 9y = 36 x - y = 4
Substituting y = 2x into the equation we get:
x - 2x = 4 -x = 4 x = -4
But x cannot be negative, so there must be a mistake. Let's try again:
The difference between a two-digit number and the number obtained by interchanging the digits is 36 means:
10x + y - (10y + x) = 36 9x - 9y = 36 x - y = 4
But we know that y = 2x, so let's substitute:
x - 2x = 4 -x = 4 x = -4
Again, x cannot be negative. It seems there's a mistake in the problem statement, as the given conditions lead to an impossible result. The correct answer should be "none".
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