The difference between a two-digit number and | vedclass

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(B) Let the tens digit be $x$ and the units digit be $y$.The number is $10x + y$.After interchanging the digits,the new number is $10y + x$.Given the

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Let the tens digit be $x$ and the units digit be $y$.The number is $10x + y$.After interchanging the digits,the new number is $10y + x$.Given the ratio of the digits is $x:y = 1:2$,so $y = 2x$.The difference between the numbers is $|(10x + y) - (10y + x)| = 36$.$|9x - 9y| = 36 \Rightarrow |x - y| = 4$.Since $y = 2x$,we have $|x - 2x| = 4 \Rightarrow |-x| = 4 \Rightarrow x = 4$.Then $y = 2(4) = 8$.The number is $48$.Sum of the digits $= x + y = 4 + 8 = 12$.Difference of the digits $= y - x = 8 - 4 = 4$.The difference between the sum and the difference of the digits is $12 - 4 = 8$.

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 $1:2$?

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