one of two digit of a two digit number is 5 time other digit if we interchange the digit of is two digit number the resulting new number is 6 more then thrice theoriginal number find two digit original two digit number

clearly the smaller digit is 1, since the larger digit cannot be greater than 9.

The number must be 15

Check:
51 = 6+3*15

To find the original two-digit number, let's assume that the tens digit is x and the units digit is y.

According to the given information:
"One of the digits is five times the other digit."

This can be expressed as an equation: x = 5y

"When we interchange the digits of the two-digit number, the resulting new number is 6 more than thrice the original number."

Let's arrange the digits in their original order as xy, which represents the original number.
When we interchange the digits, the new number becomes yx.

The equation can be written as: 10y + x = 3(10x + y) + 6

Now we can solve the system of equations to find the value of x and y.

Substituting the value of x from the first equation into the second equation:
10y + 5y = 3(10(5y) + y) + 6
15y = 3(50y + y) + 6
15y = 3(51y) + 6
15y = 153y + 6
15y - 153y = 6
-138y = 6
y = -6/138
y = -1/23

However, the value of y should be a whole number since it represents a digit in the original number. Therefore, the given information may not provide a valid solution.

Please double-check the given information to ensure its accuracy.