Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two digit number?
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Answer 1

Answer:

Let the unit place be x . Then,

tens place = 9 - x

& original number = 10 (9-x) + x

= 90-10x+x

After interchanging of the digits , the resulting two digit number will be 10x+9-x

It is given that the sum is 27. Therefore,

10x + 9 - x = 90 - 10x + x +27

or, 9x + 9 = 117 - 9x

or, 9x + 9x = 117 - 9

or, 18x = 108

or, x = 108/18

x = 6

so, original number = 90 - 10x + x

= 90 - 9x = 90 - 9 × 6

= 36

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 10(9 – x) + x

Let us reverse the digit

the number becomes 10x + (9 – x)

As per the given condition

10x + (9 – x) = 10(9 – 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