A swimming pool has 3 drain pipes. The first | vedclass

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

Question

(A) Let the time taken by pipe $A$ be $x$ hours. Since pipe $A$ takes half the time of pipe $B$,the time taken by pipe $B$ is $2x$ hours.The combined

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(A) Let the time taken by pipe $A$ be $x$ hours. Since pipe $A$ takes half the time of pipe $B$,the time taken by pipe $B$ is $2x$ hours.The combined rate of pipes $A$ and $B$ is $\frac{1}{x} + \frac{1}{2x} = \frac{3}{2x}$.According to the problem,this combined rate is twice the rate of pipe $C$ (since they take half the time of $C$). Therefore,the rate of pipe $C$ is $\frac{1}{2} 	imes \frac{3}{2x} = \frac{3}{4x}$.Together,all three pipes take $6$ hours $40$ minutes,which is $6 + \frac{40}{60} = 6 + \frac{2}{3} = \frac{20}{3}$ hours.The combined rate of all three pipes is $\frac{1}{x} + \frac{1}{2x} + \frac{3}{4x} = \frac{1}{20/3} = \frac{3}{20}$.Solving for $x$: $\frac{4+2+3}{4x} = \frac{3}{20} \Rightarrow \frac{9}{4x} = \frac{3}{20}$.$12x = 180 \Rightarrow x = 15$ hours.

Similar Questions

An outlet pipe can empty a cistern in $3$ $h$. In what time (in $h$) will the pipe empty two-third part of the cistern?

Two taps $A$ and $B$ can fill a water tank in $20$ $min$ and $24$ $min$ respectively,and a third tap $C$ empties the tank at a rate of $3$ $gallons$ per $min$. If all three taps $A$,$B$,and $C$ are opened together,the tank is filled in $15$ $min$. What is the capacity of the tank in $gallons$?

$A$ water tank is two-fifth full. Pipe $A$ can fill a tank in $10$ minutes,and pipe $B$ can empty it in $6$ minutes. If both the pipes are opened,how long will it take to empty or fill the tank completely?

$A$ 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 $24$ $minutes$ and $30$ $minutes$,respectively. There is also an outlet $C$. If all the three pipes are opened together,the cistern is full in $20$ $minutes$. How much time (in $minutes$) will be taken by outlet $C$ to empty the full cistern?

Vedclass Test Series

Exam Paper Generator

Online Exam Module