The sum of two numbers is 400. If the first number is decreased by 20% and the second number is decreased by 15%, then the sum would be 68 less. Find the numbers after the decrease.

First number  is x.
If it decreased by 20%, then 80% will be left and we will have 0.8x.

Second number is y.
If it decreased by 15%, then 85% will be left and we will have 0.85y.

Sum of x and y.
x+y=400

When x and y decreased, their sum is
0.8x+0.85y=400 - 68=332

We can write a system of equations.
x+y=400
0.8x+0.85y= 332

To solve, we can use substitution 
x=400  - y
0.8(400-y)+0.85y=332
320 - 0.8y + 0.85y =332
0.05y=332-320
0.05y=12
y=12/0.05
y = 240

x= 400-240= 160
x= 160

Check:
0.8x+0.85y=332
0.8*(160) + 0.85*240=332
332=332 True

x=160, y=240