The sum of a two digit number is 12 when interchanged the number decreases by 36 find the number

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Let the number be 10a+b where a and b are the digits.

a+b=12 (1)

10a+b-(10b+a)=36

9(a-b)=36, so a-b=4 (2)

Add (1) and (2): 2a=16, a=8 therefore b=4 and the number is 84.

CHECK: 8+4=12, 84-48=36. OK.
by Top Rated User (1.2m points)

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