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 :none486
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 :none486
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. So, we can write the equation:
10x + y - (10y + x) = 36 9x - 9y = 36 x - y = 4
Substituting y = 2x into the equation gives:
x - 2x = 4 -x = 4 x = -4
But x cannot be negative, so there must be a mistake. The correct equation should be:
10x + y - (10y + x) = 36 9x - 9y = 36 x - y = 4
Substituting y = 2x into the equation gives:
x - 2x = -4 -x = -4 x = 4
Then y = 2x = 8.
The difference between the sum and the difference of the digits is:
(x + y) - (x - y) = (4 + 8) - (4 - 8) = 12 - (-4) = 16.
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