Two pipes A and B can fill a water tank in 10 | 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 $V$ gallons.Rate of pipe $A = \frac{V}{10}$ gallons/min.Rate of pipe $B = \frac{V}{12}$ gallons/min.Rate of pipe $

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) Let the capacity of the tank be $V$ gallons.Rate of pipe $A = \frac{V}{10}$ gallons/min.Rate of pipe $B = \frac{V}{12}$ gallons/min.Rate of pipe $C = -6$ gallons/min (since it empties the tank).When $A, B,$ and $C$ are opened together,the net rate is $\frac{V}{20}$ gallons/min.Therefore,the equation is: $\frac{V}{10} + \frac{V}{12} - 6 = \frac{V}{20}$.Rearranging the terms: $\frac{V}{10} + \frac{V}{12} - \frac{V}{20} = 6$.Taking the least common multiple $(LCM)$ of $10, 12,$ and $20$,which is $60$:$\frac{6V + 5V - 3V}{60} = 6$.$\frac{8V}{60} = 6$.$\frac{2V}{15} = 6$.$V = \frac{6 	imes 15}{2} = 45$ gallons.Thus,the capacity of the tank is $45$ gallons.

Two pipes $A$ and $B$ can fill a water tank in $10$ and $12$ $min,$ respectively,and a third pipe $C$ can empty it at the rate of $6$ $gallons$ per $min.$ If $A, B,$ and $C$ are opened together,they fill the tank in $20$ $min.$ What is the capacity (in $gallons$) of the tank?

Similar Questions

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.

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in $36$ minutes,then the slower pipe alone will be able to fill the tank in (in minutes):

Having the same capacity,$9$ taps fill up a water tank in $20$ minutes. How many taps of the same capacity are required to fill up the same water tank in $15$ minutes?

Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in $3 \, h$ and $4 \, h$, respectively. The full cistern is emptied by the third tap in $5 \, h$. If all three taps are opened simultaneously, the empty cistern will be filled up in?

$A$ tap drips at a rate of $1$ drop/sec. If $600$ drops make $100 \text{ ml}$,the number of litres wasted in $300$ days is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module