In a 2-digit number unit's digit is 5 more than the ten's digit. If 5 times the given number is 24 more than two times the number obtained by interchanging the digits of the given number, then the given number is:

38

Let us consider that ,

Unit digit = a

and tens digit is = b

unit's digit is 5 more than the ten's digit

a = 5 + b

So number is 10b + b + 5 = 11b + 5

On interchanging the digits = 50 + 11b

According to question ,

5 ( 11b + 5 ) = 2 ( 50 + 11b ) + 24

55b + 25 = 100 + 22b + 24

33b = 99

b = 3

and a = 5 + 3 = 8

So number is ---->  38