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Let us suppose there had been "x" number of coconuts initially.
The first friend finds that the number is not a multiple of five, and so has to give one away to the monkey. So, now there are x-1 coconuts. He, then, takes one-fifth of his share and what remains is 4(x-1)/5 coconuts.
The second friend gives one coconut to the monkey. The number of coconuts that remains is 4(x-1)/5 - 1, or (4x - 9)/5. He takes his one-fifth share, and the number of coconuts left is 4/5 [(4x - 9)/5], or (16x - 36)/25.
The third gives one coconut to the monkey, so the number of coconuts remaining is (16x - 36)/25 - 1, or (16x - 61)/25. He takes one-fifth of his share. The number of coconuts that are left is 4/5 [(16x - 61)/25], or (64x - 244)/125.
Now it is the fourth friend's turn. He gives away one coconut to the monkey which leaves (64x - 244)/125 - 1, or (64x - 369)/125 coconuts. He takes one-fifth of his share and so four-fifths of (64x - 369)/125 remain. The number of nuts remaining is, therefore, 4/5 [(64x - 369)/125], or (256x - 1476)/625.
Finally, we come to the fifth friend. He gives away one coconut to the monkey and that leaves (256x - 1476)/625 - 1, or (256x - 2101)/625. He takes on-fifth of his share, or 1/5 [(256x - 2101)/625], or (256x - 2101)/3125.
Now, one-fifth of the share is 255. Therefore, (256x - 2101)/3125 = 255.
So, 256x - 2101 = 796875.
Thus, 256x = 798976. So, x = 3121. There were, therefore, 3121 coconuts initially. Did I get that right?
Some useful links for
- Union Public Service Commission - www.upsc.gov.in
- IIT-Kharagpur - www.iitkgp.ac.in
- Indian Statistical Institute - www.isical.ac.in
- Indian Institute of Technology Madras - www.iitm.ac.in
- Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
- Indian Institute of Mass Commission - www.iimc.nic.in
- IIT Bombay - www.iitb.ac.in
- Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
- Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
- Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
- Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
- Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
- Tata Institute of Social Sciences, Mumbai - www.tiss.edu