Dave and Diana at work

Time taken if both worked together = T
Ratio of Dave : Diana = (20 + T) : (5 + T)

We can setup the following work equation:

1/(T+5) + 1/(T+20) = 1/T
(25 + 2T)/((20+T)(5+T)) = 1/T
25T + 2T^2 = 100 + 25T + T^2
T^2 = 100
T = 10

Therefore ratio = (20 + 10) : (5 + 10) = 30:15 = 2:1

Choose B.

-BM-

Let the time taken when Dave and Diana work together be x hrs.
Given that time taken by Dave alone = x+20hrs
and time taken by Diana alone = x+5 hrs.

Instead of going for a traditional way you can answer it quickly with a simple logic.

Dave and Diana together = xhrs
Dave alone= x+20.

Now from these two statements we can conclude that, work done by Dave in 20 hrs is done by Diana in x hrs. So Dave:Diana=20:x

Similarly,
Dave and Diana together = xhrs
Diana alone = x+5,
We can conclude that work done by Diana in 5 hrs is done by Dave in x hrs. So Dave: Diana = x:5

So we have 20/x = x/5
i.e x =10.

Hence the time ratio of Dave and Diana = 20:x = 2:1