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The candles had burnt for 3 hours and 45 minutes.
The candles, initially, are of the same length, say, "L" units (centimetres, or inches). Let us suppose that the candles had burnt for "t" minutes before lights came on.
The fat candle is supposed to burn for five hours (300 minutes), so in one minute L/300 units (centimetres, or inches) of that candle burns off. In "t" minutes, tL/300 units of the candle burns off and the length of the candle remaining is L - tL/300.
The slender candle is supposed to burn for four hours (240 minutes), so in one minute L/240 units of that candle burns off. In "t" minutes, tL/240 units of this candle burns off and the length of the candle remaining is L - tL/240.
Now the fat candle is four times longer than the slender one.
So, L - tL/300 = 4(L - tL/240)
So, L - tL/300 = 4L - tL/60.
Thus, tL/60 - tL/300 = 4L - L.
So, (5tL - tL)/300 = 3L.
Therefore, 4tL/300 = 3L.
So, 4tL = 900L.
That gives us, 4t = 900. So, t = 225.
Thus, the candles had burned for 225 minutes. So, the power failure had lasted for 3 hours and 45 minutes.
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