I have seen a lot video in internet,by doing push-ups chest can become more bigger.Which workouts could give grow results on chest area,by different push-ups?
It's all about straining the muscles and recovery.
I do sets of 25 pushups, but with three rests of about 20 sec within each set. Those micro-rests are important for muscle recovery (stuff like oxygen, glycogen, lactate). In a training session I do 100 to 150 pushups in sets of 25, mixed in with other (mostly aerobic) exercise.
Try that for 6 weeks and you should see a definite improvement.
For chest hypertrophy usual recommendation is weight lifting, not push-ups. That is because there is very little overload when you do push-ups, you basically training endurance at the point of 100s of pushups.
Weightlifting (exercises such as bench press with barbell/dumbbells, flies with dumbbells) allow you to more efficiently utilize your time and see increase in muscle mass faster.
Regardless of what workout you choose, you should start tracking your progress. Use measuring tape to know whether your workout works or not. When chest stop growing -- time to switch workout