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The sum of the two digits of a two-digit number is 13 and the number obtained by interchanging the two digits is 27 less than the original number. What is the original number?

The sum of the two digits of a two-digit number is 13 and the number obtained by interchanging the two digits is 27 less than the original number. What is the original number? Correct Answer 85

Let the unit digit of the two-digit number be y and the tens place digit be x.

Then the two digit number is = 10x + y

By interchanging the digits, we get = 10y + x

Therefore, according to the question,

x + y = 13

And,

10y + x = (10x + y) - 27

9y = 9x - 27

y = x - 3

Substituting the value of y in above equation we get,

x + (x - 3) = 13

2x - 3 = 13 

x = 16 ÷ 2

x = 8

Now, by substituting this value of x, we get

y = 8 - 3

y = 5

Therefore, the two digit original number = 10x + y

= 10 × 8 + 5

= 80 + 5

= 85

Hence, 85 is the correct answer.

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