Brain Teasers

1. Coin Puzzle: Here is yet another variation on the coin weighing puzzle. There are 101 coins, 50 of them good, and the rest (51) are faulty. The faulty ones all weigh the same: they are either one gram heavier or one gram lighter than the good ones. You have a balance (with no weights) which, in a weighing, can tell you which side is heavier and by how much. I take one coin out and want to find out whether it is good or faulty by just using the balance only once. Is that possible? If so, how? If not, why not?

2. Two friends went to the market to buy watermelons. There were two types, both round. The small one cost Rs 20 and the big one Rs 100. The big one was twice as big as the small one (twice the diameter). Ramu said, "I have Rs 40 so I will buy two small ones." The other friend Shyamu told him, "I have Rs 60. Why don't we buy one big one and share : you take 2/5 and I'll take 3/5." 
Will Ramu be better off just buying two small melons or should he take up his friend's offer?