Question

The sum of digits of a two digit number is 9 the number obtained by interchanging the digits exceeds the given number by 27 find the number.

Answer 1

Answer:

Let the two digit number be 10x + y

Given that the sum of the digits is 9

x + y = 9 (equation 1)

Given that the number obtained by interchanging the digits exceeds the given number by 27

10y + x = 10x + y + 27 

9x - 9y = - 27

taking 9 as common

x - y = - 3 (equation 2)

Adding equation 1 and 2

x + y = 9

x - y = - 3

2x = 6

x = 3

3 + y = 9

y = 6

The number is 10x + y is 36.

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Answer 2

Answer:

Let the two digits of the no. be x and y,

then, the no. = 10x + y

And,

x + y = 9 (given)

After interchanging the digits, the no. obtained is = 10y + x

Given,

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

10y + x = 27 + 10x + y

10y - y = 27 + 10x - x

9y = 27 + 9x

9y - 9x = 27

9 (y - x) = 27

y - x = 27/9 = 3

So we have got two equations:

x + y = 9 and, y - x = 3

Adding both the equations,

(x + y) + (y - x) = 9 + 3 = 12

2y = 12

y = 6

Now, putting the value of y in 1st equation,

x + y = 9

x + 6 = 9

x = 9 - 6 = 3

So, x = 3, y = 6

Now, the number is = 10x + y

Now, the number is = 10x + y= 10 × 3 + 6 = 36

I hope you understood :)