For the charities - Shakuntala Devi Puzzle

I tried to solve a puzzle today, that I stumbled upon, after a long hiatus. For starters I found my Quant skills to be missing. Only to realize later that what I really was missing was being organized.

Puzzle from 'Puzzles To Puzzle You' by 'Shakuntala Devi'

For The Charities (45):

One day when I was walking on the road in NewDelhi, a group of boys approached me for donationfor their poor boys' fund. I gave them a rupee morethan half the money I had in my purse. I must havewalked a few more yards when a group of womenapproached me for donation, for an orphanage. I gavethem two rupees more than half the money I had inmy purse. Then, after a few yards I was approached bya religious group for a donation to the temple theywere building. I gave them three rupees more than half of what I had in my purse.At last when I returned to my hotel room, I foundthat I had only one rupee remaining in my purse.How much money did I have in my purse when I started?

Solution:

I found the best way to go about solving this one would be to have two columns. 1. Current balance. and 2. Money given for charities. The key is to keep track of money remaining after donating some to charity each time.

1. Let's say the original amount money in purse to start with was 'n'. -- Col1
2. Charity money donated to boys fund was n/2 +1 = (n+2)/2. -- Col2
3. Money remaining is (n - (n+2)/2) = (n-2)/2. -- Col1
4. Charity money donated to women's fund was ((n-2)/2/2 + 2) = (n+6)/4 -- Col2
5. Money remaining is (n-2)/2 - (n+6)/4 = (n-10)/4 -- Col1
6. Charity money donated to temple fund was (n-10)/4/2 + 3 = (n+14)/8 -- Col2
7. Money remaining is (n-10)/4 - (n+14)/8 = (n-34)/8 -- Col1

The last fraction's value is given to be '1'. From this it can be deduced that the value of n is 42. Thus, the original amount of money in the purse was INR 42.

All that is required to know to solve this puzzle is basic fractions know-how and being organized.

Let there be peace. .::V::.
Cheers to Life!
~M~