It does not matter if you do the push up first or the pull ups. Here's how it works:
Start your clock. During the first minute do one pull up. During the second minute do two pull ups, during the third minute do 3 pull ups. Keep doing this until you can no longer do the correct amount of pull ups in the one minute time frame.
Start your clock. During the first 30 seconds do one push up. During the second 30 second period do two push ups. You get the point.
Post level of push ups and pull ups to comments. You will be surprised by the total number of reps done.