Does all your work go to waste or the mining continues from the last place you left. Lets say I am about to get a block solved and there is a power cut, how does it hamper my mining and the rewards.
If your power is cut (and consequently you lose your internet connection), your miner won't be able to either finish "solving the block" (because it will be powered off).
Even if your miner finishes confirming the transaction, it would not be able to broadcast the confirmation to the network (assuming your internet is down).
By the time power/internet is restored, you will be well past the average block confirmation time of about 15 seconds: https://ethstats.net/
So the confirmation will likely have been confirmed by other miners already.
It is possible to confirm the transaction and claim a reward if the transaction fee is low enough that other miners lack financial incentive to mine it. But at that point there'd be no incentive for you to mine it either.
I think you might be misunderstanding how mining works somewhat. There isn't really a "place you left" in the sense you're probably thinking about it. There isn't a notion of progress when it comes to mining. You either found a block or you didn't. Like when you flip a coin, you either get a head or a tail; if you flip three heads in a row, you are no closer to getting a tail next time. Mining is a bit like flipping a coin until you get a tail and then advertising that fact.
If your power goes out between when you found a block and when it is broadcast to the network, your work is lost. Otherwise, it's the same as not having found any blocks during the period of time you have no power.
If you lose power for half the day, whatever the pattern is, it's the same as having half your peak hash power (assuming no rise in difficulty).