Two pipes can fill a cistern separately in 24 | vedclass

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Question

(C) Let the capacity of the cistern be $C$ litres.Rate of the first pipe $= \frac{C}{24}$ litres/minute.Rate of the second pipe $= \frac{C}{40}$ litre

Vedclass · Accepted Answer

$600$

Vedclass · Answer

(C) Let the capacity of the cistern be $C$ litres.Rate of the first pipe $= \frac{C}{24}$ litres/minute.Rate of the second pipe $= \frac{C}{40}$ litres/minute.Rate of the waste pipe $= -30$ litres/minute.When all three pipes are open,the cistern fills in $1$ hour ($60$ minutes).Therefore,the net rate of filling is $\frac{C}{60}$ litres/minute.Equation: $\frac{C}{24} + \frac{C}{40} - 30 = \frac{C}{60}$.Rearranging the terms: $\frac{C}{24} + \frac{C}{40} - \frac{C}{60} = 30$.Taking the $LCM$ of $24, 40,$ and $60$,which is $120$:$\frac{5C + 3C - 2C}{120} = 30$.$\frac{6C}{120} = 30$.$\frac{C}{20} = 30$.$C = 30 	imes 20 = 600$ litres.Thus,the capacity of the cistern is $600$ litres.

Two pipes can fill a cistern separately in $24$ $minutes$ and $40$ $minutes$ respectively. $A$ waste pipe can drain off $30 \text{ litres per minute}$. If all the three pipes are opened,the cistern fills in one $hour$. The capacity (in $litres$) of the cistern is:

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