Question

The sum of the digits of a 2-digit number is 9.If 27 is added to the number, the digits are reversed. find the number

Answer 1

Answer:

number is 36

Step-by-step explanation:

let the number be 10x + y

according to question,

x + y=9

also,  10x + y + 27 = 10y + x

solve them

the answer is x=3, y=6

Answer 2

Let the digit at ten's place = x

Let the digit at unit place = y

Number = 10x + y

1st Condition :

x + y = 9 ...(1)

2nd Condition :

10x + y + 27 = 10y + x

10x - x + 27 = 10y - y

9x + 27 = 9y

9x - 9y = - 27

9y - 9x = 27

y - x = 3 ...(2)

y = x + 3 ...(3)

put the value of equation (1)

x + y = 9

x + x + 3 = 9

2x + 3 = 9

2x = 9 - 3

2x = 6

x = 6 / 2 = 3

x = 3

put the value of equation (3).

y = x + 3

y = 3 + 3

y = 6

The Digit at Ten's Place = x = 3
The Digit at Unit Place = y = 6

The Number = 10x + y

= 10(3) + 6 = 30 + 6

= 36

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