Question

The sum of the digit of 2-digit number is 13 and the difference between the number and that formed by reversing the digit is 27 . Find the number.

Answer 1

The number is 85.

Let the digit in ones place be x

Let the digit in tens place be y

Then, the number formed is 10x+y

Also, the number formed by reversing the digits of Original Number will be 10y+x

___________________________

According to the Question,

x+y = 13 ______(1)

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

=> 9x - 9y = 27

=> 9(x-y) = 27

=> x-y = 3______(2)

Adding equation(1) and equation(2) we get,

2x = 16

x = 8

Putting value of x in equation(2) we get,

8-y=3

=> -y=-5

=> Y = 5

Hence, the number is 10x + y

=> 10(8) + 5

=> 80 + 5

=> 85

Answer 2

Let the digit in the tens place be x and the digit in the ones place be y.

⇒ The number is (10x + y)

Given that the sum of the digit is 13

⇒ x + y = 13

⇒ x = 13 - y

The difference between the number and that formed by reversing the digit is 27

⇒ (10x + y) - (10y + x) = 27

⇒ 10x + y - 10y - x = 27

⇒ 9x - 9y = 27

The two equations are:

x = 13 - y -------------------------------------- [ 1 ]

9x - 9y = 27 -------------------------------- [ 2 ]

Sub equation [ 1 ] into [ 2 ]:

9(13 - y) - 9y = 27

117 - 9y - 9y = 27

18y = 90

y = 5 -------------- sub into [ 1 ] to find x

Find x:

x = 13 - y

x = 13 - 5

x = 8

Find the number:

Number = 10x + y = 10(8) + 5 = 85

Answer: The number is 85