Let x = the amount in fund A.
Let y = the amount in fund B.
Interest fund A = 4% = 0.04
Interest fund B = 10% = 0.10
Then, according to the information given we have that:
x + y = 55000
And the formula for determining simple interest is given by:

Where:
P = initial capital
R = interest rate
T = time
We have the following equation

Next, we solve the system of two equations.
From the first equation we clear x:

Substitute x in the second equation:

Simplify

Solve for y:

Then, for x:

Answer:
Fund A = $44000
Fund B = $11000