Buy a Mach City iBIKE - single speed.... its pretty sturdy but also very-light... i just sold off my SCHNELL and bought it ... rides pretty well too.
However, if you're looking to add a bit more class .. then go for Mach City Munich.... it's like a entry level racing/hybrid cycle which can really run... its heavier than the iBike...but boy does it look cool.
Those are very common nowadays... herein in gujarat they're everywhere... thanks to the parent company being BSA HERCULES.. :-D
i dunno... i hear hero sprint is pretty cool for city riding..other than the machcity series... and ofcourse you can always pick up the cool...funky...geared...with mono/dual shock MTBS available from hercules or hero ... the new rodeo bikes are very cool...
Nevertheless, there will be other bikes in SCHNELL, DODGE, KROSS, etc.... but try to keep them 2nd priority...
I would want you to go with a MTB or a hybrid. Because, you say that a part of the road will be rough. Daily commuting with a bike like a city one will prove to be a hassle for the tyres. Nevertheless to say, I've ridden the Mach City and found it smooth. Still, I wouldn't recommend it for off roading things, even for a bit. For your budget, under 10k, I think the best one I could find is Hercules Roadeo Riot 26". It looks sturdy, feels sturdy and pedalling isn't a menace at all. It's smooth on flat surfaces and well equipped to handle rough terrain and off roads. Surprisingly, I clocked around 36 kmh so you can expect the bicycle to be swift. You have my word for it. Finally, go with the bicycle that you find to be fit for you.
Have you considered a BtWin Rockrider?
Also, if you have a *strict* 10k budget, please set aside about Rs 1.5k for a helmet. Some amount also for locks, stands etc. unless you can bargain hard and get the seller to throw these in for free. Choose your own good quality helmet. Even if you can bargain a helmet into the deal, avoid it. Most dealers will care more about their margins than your head's safety.