Everyone here is advising to send coins with higher fees. But can anybody explain how do I increase the amount of fee if I want to send coins from exchanges like Poloniex, Bittrex etc. where the fees are automatically decided & there is no option to change the fees manually even in the setting menu? 
Exchanges usually pay appropriate fee. You don't need to worry!
If you are using exchanges or online wallets, I highly recommend you to use offline wallets. There are a few online wallets which are "okay", but use them at your own risk! You *won't* have full control over your bitcoins!