Let's say,
The investment1 = x
investment2 = y
As given, two investments totaling to 8000$. Therefore,
x + y = 8000. (i)
The net loss on investment x (4%) = - 4% of x = - 4/100 * x = - 0.04x
The net profit on investment y (6%) = 6% of x = 6/100 * x = 0.06x
As given, the net receipt is = 400$
Therefore,
-0.04x + 0.06y = 400. (ii)
Now, solve both equations simultaneously.
from eq (1), x = 8000 - y. Put this in eq(ii).
-0.04(8000 - y) + 0.06y = 400
-320 + 0.04y + 0.06y = 400
0.1y = 400 + 320
0.1y = 720
Multiply both sides by (10), we get
10* (0.1y) = 10 * 720
y = 7200
Now, put the value of y in eq (i) and get the value of x
x + y = 8000
x + 7200 = 8000
x = 800
Hence, the first investment is 800, while the second is 7200.