Will the battery capacity improve if i use a original apple charger for my iphone 4?

I lost my original apple charger + data cable recently. I purchased a fake set for rs 200 and strated using it. However, i see that it charges the phone quiet quickly but the battery drains very quickly too.

No. The charger simply provides power. The charge regulation circuits are in the phone. If your battery is draining quickly then the battery is old and should be replaced.