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The cook sets the the two hour glasses simultaneously. The sand grains in the small hour glass drain out completely in four minutes.
So, four minutes have elapsed. At this point of time there is three minutes of sand in the upper half of the bigger hour glass. The cook quickly inverts the smaller hour glass and it starts "ticking" again. After three minutes, the big hour glass empties completely, and the total time measured is 4 + 3 = 7 minutes. There is still one minute of sand left in the smaller hour glass.
The cook swiftly inverts the big hour glass and sets it "ticking" again. After one minute, the small hour glass empties completely and, now, the time measured is 7 + 1 = 8 minutes. The cook now needs to measure one more minute.
At this stage, one minute worth of sand has trickled down into the lower half of the bigger hour glass, and there are six minutes of sand in its upper half. Is that right? Now, all that the cook has to do is quickly invert the bigger hour glass so that in this position one minute of sand is in the upper half and six minutes of sand is in the lower half. After one minute, the bigger hour glass empties and the cook is able to measure nine minutes quite accurately. A clever cook, really!
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