Question

sum of the digits of two digit number is 9 the number obtained by interchanging two digit exceeds the given number by 27
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Answer 1

Answer:

36 is the correct answer

Answer 2

Given:-

• The sum of the digits of a two digits is 9.
• The digits are interchanged the number obtained exceeds the original number by 27.

To find:-

• Find the number .?

Solutions:-

• Let the digits at unit's place be y.
• Let the digits at ten's place by x.

Number => 10x + y

The sum of the digits of a two digits is 9.

=> x + y = 9

=> x = 9 - y ............(i).

The digits are interchanged the number obtained exceeds the original number by 27.

=> 10y + x = 10x + y + 27

=> 10x + y + 27 - 10y - x = 0

=> 9x - 9y = -27

=> 9(x - y) = -27

=> x - y = -27/9

=> x - y = -3 ..............(ii).

Putting the value of x in Eq. 2. We get,

=> x - y = -3

=> 9 - y - y = -3

=> -2y = -12

=> y = -12/-2

=> y = 6

Putting the value of y in Eq. 1. We get,

=> x = 9 - y

=> x = 9 - 6

=> x = 3

So, Number => 10x + y

=> 10 × 3 + 6

=> 30 + 6

=> 36

Hence, the number formed is 36.