Find the two-digit number such that the sum of its digits is 8 and the digits of the number get reversed when 36 is added to it.

The sum of its digits is 8 and the digits of the number get reversed when 36 is added to it.

Let the two-digit number be 10x+y, where:

xis the tens digit, and
yis the units digit.

The sum of the digits is 8:

x + y  = 8

The number becomes reversed when 36 is added:

10x + y + 36 = 10y + x 

10x - x + y - 10y  = -36
9x - 9y = -36
x - y = -4 

Now we have two equations:

x + y = 8  .....(1)
x - y = -4  .....(2)

Add equation (1) and (2),

x + y + x - y = 8 + 4

2x = 12

x = 6

Substitute = 2 in equation (1),

2 + y = 8

 y = 8 - 2

 y = 6

The two-digit number = 10x + y = 10(2) + 6 = 26

So, The two-digit number is 26

Thus, the correct answer is (b).