Problem:
The digit at ones place of a two-digit number is 4 times the digit at tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.

Solution:
Let's solve this problem step by step.

Step 1: Understand the problem:
We are given a two-digit number. The digit at the ones place is 4 times the digit at the tens place. When the digits are reversed, the resulting number exceeds the given number by 54. We need to find the given number.

Step 2: Assign variables:
Let the tens place digit be 'x' and the ones place digit be 'y'. The given number can be represented as 10x + y.

Step 3: Formulate the equations:
From the problem statement, we can derive two equations:
1. y = 4x (the digit at ones place is 4 times the digit at tens place)
2. (10y + x) - (10x + y) = 54 (the number obtained by reversing the digits exceeds the given number by 54)

Step 4: Solve the equations:
Let's solve the equations to find the values of 'x' and 'y'.

Equation 1:
y = 4x

Equation 2:
(10y + x) - (10x + y) = 54
10y + x - 10x - y = 54
9y - 9x = 54
9(y - x) = 54
y - x = 6

Step 5: Substitute and solve:
Substitute the value of 'y' from equation 1 into equation 2:
4x - x = 6
3x = 6
x = 2

Substitute the value of 'x' into equation 1 to find 'y':
y = 4(2)
y = 8

So, the tens place digit is 2 and the ones place digit is 8. Therefore, the given number is 28.

Step 6: Verify the solution:
Let's check if our solution is correct. The number obtained by reversing the digits is 82, which exceeds the given number 28 by 54. Hence, our solution is correct.

Answer:
The given number is 28.