Question

A number consists of two digits. The sum of the digits is 5 . If 9 is substract from the number, the digits are reversed. Find the number​

Answer 1

Let the number be 10x +y  ,

    x = ten's place  , y = one's place

x + y = 5          ---> [1]

reversed no: ,

10y + x

10x+ y + 9 = 10y+x

9x - 9y = -9

x - y = -1            ---> [2]

Adding equations 1 and 2

x + y = 5

x - y = -1

_______

2x = 4

x = 2

x -y = -1

2 - y = -1

2 + 1 = y

3 = y

the number is :-

10x + y 

10 x 2 + 3  = 23

The no: is 23

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Answer 2

Answer:

Let the number be xy.

x + y = 5

(10x + y) - 9 = 10y + x (I multiplied by 10 because of place values)

10x + y - 9 = 10y + x

9x - 9y = 9

x - y = 1

So, now we know x+y = 5 and x - y = 1

x + y = 5

x - y = 1

+_________

2x = 6

x = 3

x + y = 5

3 + y = 5

y = 2

The number is 32.

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