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  4. A tap supplies water at 15° C and another tap connected to geyser supplies water at 95° C. How much hot water must be taken so as to get 60 kg of water at 35° C ?

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Q. A tap supplies water at $15^{\circ} C$ and another tap connected to geyser supplies water at $95^{\circ} C$. How much hot water must be taken so as to get $60\,kg$ of water at $35^{\circ} C ?$

Uttarkhand PMTUttarkhand PMT 2011

Solution:

Let $ x \, kg$ of hot water be taken than cold water taken is
$ (60-x)\,kg $ . Using heat gained = heat lost
$ x\times 1000\times (95-35)=(60-x)\times 1000 $
$ \times (35-15) $
$ x\times 1000\times 60=(60-x)\times 1000\times 20 $
$ 3x=60-x $
$ 4x=60 $
$ x=\frac{60}{4}=15\,kg $