If you are looking for improve your upper body fast then instead doing normal pushups better try weighted push ups for faster improvement in your upper body.
How to do Weighted Push Ups Properly?
Step 1. Start with standard push-up position with hands and feet wider than shoulder-width apart, With Weight Plate on your back. Step 2. Breathe in and Lower yourself until your chest almost touches the floor and hold down for contraction Step 3. Keep your back and hips in one alignment, Elbows should be completely locked out Step 4. Now Breath out, Squeeze your chest muscle and press your body back up Step 5. Repeat the same for complete the repetitions
Important Key Points:
You must have intermediate to advance level before do this exercise.