Two pipes can fill a cistern separately in 24 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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:

Similar Questions

Two pipes $A$ and $B$ can separately empty a cistern in $12$ $hours$ and $15$ $hours$,respectively. In what time will the cistern be emptied,if both the pipes are opened together?

Three taps $A, B$ and $C$ together can fill an empty cistern in $10$ $min.$ The tap $A$ alone can fill it in $30$ $min$ and the tap $B$ alone can fill it in $40$ $min.$ How long will the tap $C$ alone take to fill it? (in $minutes$)

Two pipes,$A$ and $B,$ can separately fill a tank in $6$ $hours$ and $8$ $hours,$ respectively. Both the pipes are opened together,but $1 \frac{1}{2}$ $hours$ later pipe $A$ is turned off. How much time (in $hours$) will it take to fill the tank?

$A$ leak in the bottom of a tank can empty the full tank in $8$ $hours$. An inlet pipe fills water at the rate of $6$ $litres$ a minute. When the tank is full,the inlet pipe is opened and due to the leak,the tank is empty in $12$ $hours$. How many litres does the tank hold?

Two pipes $A$ and $B$ can fill a cistern in $4$ $minutes$ and $6$ $minutes,$ respectively. If these pipes are turned on alternately for $1$ $minute$ each,then how long will it take for the cistern to fill?

Vedclass Test Series

Exam Paper Generator

Online Exam Module