Question

IAS Level question : There are 10 bags. Each bag contains 10 coins and each coin weighs 10gms. However there is one wrong bag that contains all coins of 9 gms each. You need to identify the wrong bag. U are given a digital weighing scale & u are allowed to weigh full bag(s) or weigh coin(s) taken frm one or more bags. After using the weighing scale ONLY ONCE, u need to identify the wrong bag. How would u do this?

Answer 1

If there is only 1 bag with forgeries, then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag and simply weigh the picked coins together ! 

If there were no forgeries, you know that the total weight should be (1+2+3+ . . . +10) = 55 grams.

But if, for example, the weight is 55.3 grams, then you know that 3 coins are forgeries, so that must be bag 3. So, that solves it.

Now, if there is more than 1 bag with forgeries, then you will need to choose numbers that cannot be mistaken when added together. One possibility is: 1, 2, 4, 10, 20, 50, 100, 200, 500 and 1000.

Hope it helps...☺