How to do this?

Question

Sum of the digits of a two-digit number is 9. The given number obtained by interchangingthe digits exceeds the given number by 27. What is the number?

Answer 1

Sum of two digits is 9
Let the unit digit be x
Therefore, tens digit =9-x

The original number = 10(9-x)+x
= 90-10x+x
= 90-9x

By interchanging the digits the new number = 10x+(9-x)
= 10x+9-x
= 9x+9

According to question
9x+9>90-9x

Then,
9x+9-27 = 90-9x
9x-18 = 90-9x
9x+9x = 90+18
18x = 108
x = 108/18 = 6

Unit digit is = 6
Therefore, Tens digit = 9-x = 9-6 = 3
Given number = 3*10+6
=36
You can cheak if by this,
Interchanging the digit the number obtained =63
The difference = 63 - 36 = 27
Which is same as ur qus

Answer 2

Say the digits of the number are a and b.
So, the written number will be like this : ab (note : this is NOT the algebraic expression "a times b", just a general representation of a two-digit number)

Next, you should realise that when we write a number like this "ab", it is simply a shorthand way of expressing the number 10a + b ( that is, ten times a plus b - the "a" in "ab" is in the tens position, right?)

So, the first number is "ab", or 10a + b;
transposing the digits gives the number "ba", or 10b + a.

We are told that 10b + a is equal to the first number plus 27. Therefore we can write the equation

10b + a = 10a + b +27

Collecting like terms, this becomes

10b - b = 10a - a + 27

or 9b = 9a + 27, which is the same as :

b = a + 3 (dividing by 9)

Further, we are told that the sum of the digits is 9, that is:

a + b = 9

which can be rearranged to give

b = 9 - a.

There are several ways of proceeding now. For example, from the discussion above we have two expressions for b :

b = a + 3 ; and b = 9 - a

Equating these two expressions for b gives

a + 3 = 9 - a

Rearranging according to the rules of algebra this becomes

a + a = 9 - 3

or 2a = 6

from which it is easy to see that, therefore, a is equal to 3; and since b = a + 3, then b must equal 6. So the number sought is 36.

Check that 36 + 27 = 63.

Answer 3

While I'm sure there is a formula or combination of formulas that would be helpful in this situation; it is probably easiest to explain as follows:

There are only 4 possible answers given the first fact:
1-8
2-7
3-6
4-5

18 & 81 are more than 27 apart, as are 27 and 72. 45 and 54 are only 9 apart, so 36 is your answer (exactly 27 less than 63).

Sometimes it is really easy to overthink a math problem. I initially tried the formula route, but couldn't come up with something that worked.

Answer 4

36

Answer 5

A simple question.
36