Question

the sum of digits of two digits number is 9 if 27 is added to its the digits of the number gets reversed then the number is​

Answer 1

let the no be X Y

x+y=9...eq(1)

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

10x-x+y-10y=-27

9x-9y= -27

9(X - Y) = -27

x-y=-3....eq (2)

add equation 1 and 2

we get X=3

substitute the value of x in the equation 1 , we get y= 6

show the number is 36

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Answer 2

Answer:

The number is 36.

Step-by-step explanation:

Given :-

• The sum of digits is 9.
• If 27 is added, the number gets reversed.

To find :-

The number

Solution :-

Let the tenth digit of the number be x and the ones digit be y.

Suppose, the number is 56.

It can be represented as 10×5 + 6.

Similarly, if the tenth digit is x, while the ones digit is y,

number = 10x + y

Reverse of 56 = 65

Reverse can be represented as 10×6 + 5.

Similarly, reverse of 10x + y will be 10y + x.

According to question,

If 27 is added to a number, the number becomes it's reversed.

So it's equation will be,

10x + y + 27 = 10y + x

On solving we get,

10x + y + 27 = 10y + x

9x - 9y = - 27

Taking 9 as common,

9(x - y) = - 27

x - y = - 3

Therefore, x - y = - 3

It is given, that the sum of digits is 9. Therefore, x + y = 9

x - y = - 3

x + y = 9

Adding these equations,

x - y + x + y = - 3 + 9

2x = 6

x = 3

We now know that x is 3.

We were given, x + y = 9

Substituting the value of x in the equation,

x + y = 9

3 + y = 9

y = 6

Hence our original number is,

10x + y

= 10×3 + 6

= 36

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