## Saturday, 6 October 2012

### Puzzle-34

Four sisters – Suvarna,Tara,Uma and Vibha are playing a game such that the looser doubles the money of each of the other players from her share.They played four games and each sister lost one game in alphabetical order. At the end of fourth game each sister had Rs.32. How much money did Suvarna start with?
(i)Rs. 60(ii) Rs. 34(iii) Rs. 66   (iv) Rs. 28
Solution:

I like this problem. It is based on logic.
At the end of four games, each had Rs.32 => total amount with all the four is 4*32 = 128
“The point is even if some money changes hands with the outcome of each game, the total money (Rs128) with all the four does not vary at any point”.
As the games were lost by the four sisters in alphabetical order, Suvarna lost the first game and after that in the remaining three games her money got doubled three times ie., “The point here is she lost only in the first game and from this point onwards, her money got multiplied 8 times after completion of the remaining 3 games”.
Let the money that Suvarna initially had with be ‘X’. So the total amount with all the other three sisters is 128-X before starting the first game. After first game, in which Suvarna lost, Suvarna must be left with X-(128-X) as she needed to give (128-X) to make double the amounts with the other three.

 Suvarna's money Total Money with other three At the start X 128-X After 1st game X-(128-X) = 2X-128 2(28-X) After 2nd game 2(2X-128) Not required to find After 3rd game 4(2X-128) Not required to find After 4th game 8(2X-128) Not required to find

Finally the amount left with Suvarna is 8(2X-128). But it is given that at the end of four games, each had Rs.32. It means Suvarna ended up with Rs 32.
=> 8(2X-128) = 32 => X = 66