Two inlet pipes can fill a cistern in 10 hour | vedclass

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

Question

(C) Let the capacity of the tank be $C$ $gallons$.Rate of the first inlet pipe $= \frac{C}{10}$ $gallons/hour$.Rate of the second inlet pipe $= \frac{

Vedclass · Accepted Answer

$600$

Vedclass · Answer

(C) Let the capacity of the tank be $C$ $gallons$.Rate of the first inlet pipe $= \frac{C}{10}$ $gallons/hour$.Rate of the second inlet pipe $= \frac{C}{12}$ $gallons/hour$.Rate of the outlet pipe $= -80$ $gallons/hour$.When all three pipes work together,the net rate is $\frac{C}{20}$ $gallons/hour$.Therefore,$\frac{C}{10} + \frac{C}{12} - 80 = \frac{C}{20}$.Rearranging the terms: $\frac{C}{10} + \frac{C}{12} - \frac{C}{20} = 80$.Taking the least common multiple $(LCM)$ of $10, 12, 20$,which is $60$:$\frac{6C + 5C - 3C}{60} = 80$.$\frac{8C}{60} = 80$.$\frac{2C}{15} = 80$.$C = 80 	imes \frac{15}{2} = 600$.Thus,the capacity of the tank is $600$ $gallons$.

Two inlet pipes can fill a cistern in $10$ $hours$ and $12$ $hours$ respectively,and an outlet pipe can empty $80$ $gallons$ of water per hour. All three pipes working together can fill the empty cistern in $20$ $hours$. What is the capacity (in $gallons$) of the tank?

Similar Questions

$A, B, C$ are pipes attached to a cistern. $A$ and $B$ can fill it in $20$ and $30$ minutes respectively,while $C$ can empty it in $15$ minutes. If $A, B, C$ are kept open successively for $1$ minute each,how soon will the cistern be filled? (in minutes)

Pipe $A$ can fill a tank in $5$ $hours$,pipe $B$ in $10$ $hours$,and pipe $C$ in $30$ $hours$. If all the pipes are opened,in how many $hours$ will the tank be filled?

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the full tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

Two pipes $A$ and $B$ can fill a tank in $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

Three pipes $A, B$ and $C$ can fill a cistern in $6$ $hrs$. After working together for $2$ $hrs$,$C$ is closed and $A$ and $B$ fill the remaining part of the cistern in $8$ $hrs$. Find the time (in $hrs$) in which the cistern can be filled by pipe $C$ alone.

Vedclass Test Series

Exam Paper Generator

Online Exam Module