Question

Sum of the digits of a two-digit number is 9. when we interchange the digits, it isfound that the resulting new number is greater than the original number by 27. whatis the two-digit number?

Answer 1

Solution:

Let x and y be the two-digit number.

x+y=9 , then we interchange it
yx-xy=27

If x=3 and y = 6, then we obtain,
3+6=9 and if we interchange it, we get the value of 27,

63-36=27.

Therefore, the two-digit number are 3 and 6.

Answer 2

Answer:

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Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = 9–x

Thus the two-digit number is 109–x + x

Let us reverse the digit

the number becomes 10x + 9–x

As per the given condition

10x + 9–x = 109–x + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36