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Question

The ratio of the tens digit to the ones digit of a 2-digit number is 2:3. If 27 is added to the number, the digits interchange their places. Find the number.

Solution
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Let the ones digit and tens digit of the number be a,b respectively.

number =ba

given that,

ba=23

3b=2ab=2a3 -------(1)

it is also given that,

ba+27=ab
(10b+a)+27=10a+b
9a9b=27
9(ab)=27
ab=3

put the value of b from equation 1

a2a3=3

3a2a=9

a=9,b=2×93=6

number =69

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