Question

sum of the digits of a two 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?​

Answer 1

Answer:

Let the digits be x and y.

Then, x+y = 9

the original number is 10x+y.

On reversing, we get the new number as 10y+x

The new number is greater than the old number by 27, i.e.

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

or 9y-9x = 27, or y-x = 3

and x+y = 9

Adding the two equations, we get 2y = 12 or y = 6.

Thus, x = 3.

Therefore, the original number is 36.

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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