Two pipes,A and B, can separately fill a cist | vedclass

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

Question

(A) Work done by pipe $A$ in $1$ minute $= \frac{1}{15}$.Work done by pipe $B$ in $1$ minute $= \frac{1}{18}$.Work done by pipes $(A+B)$ in $6$ minute

Vedclass · Accepted Answer

$16 \frac{1}{2} 	ext{ minutes}$

Vedclass · Answer

(A) Work done by pipe $A$ in $1$ minute $= \frac{1}{15}$.Work done by pipe $B$ in $1$ minute $= \frac{1}{18}$.Work done by pipes $(A+B)$ in $6$ minutes $= 6 	imes (\frac{1}{15} + \frac{1}{18}) = 6 	imes (\frac{6+5}{90}) = 6 	imes \frac{11}{90} = \frac{11}{15}$.So,$\frac{11}{15}$ of the cistern is filled in $6$ minutes.Now,all three pipes $(A+B+C)$ are opened. The net work done in $1$ minute $= \frac{1}{15} + \frac{1}{18} - \frac{1}{6} = \frac{6+5-15}{90} = \frac{-4}{90} = -\frac{2}{45}$.The negative sign indicates that the cistern is being emptied at a rate of $\frac{2}{45}$ per minute.Time taken to empty $\frac{11}{15}$ of the cistern $= \frac{11/15}{2/45} = \frac{11}{15} 	imes \frac{45}{2} = \frac{33}{2} = 16 \frac{1}{2}$ minutes.

Similar Questions

If two pipes function simultaneously,the reservoir will be filled in $6$ $hours$. One pipe fills the reservoir $5$ $hours$ faster than the other. How many hours does the faster pipe take to fill the reservoir?

$A$ cistern has $3$ pipes $A, B$ and $C$. Pipes $A$ and $B$ can fill it in $3$ and $4$ hours respectively,and pipe $C$ can empty it in $1$ hour. If the pipes are opened at $3 \text{ pm}$,$4 \text{ pm}$,and $5 \text{ pm}$ respectively on the same day,at what time will the cistern be empty?

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.

Two pipes $A$ and $B$ can fill a tank in $1$ $h$ and $75$ $min,$ respectively. There is also an outlet $C$. If all the three pipes are opened together, the tank is full in $50$ $min.$ How much time (in $minutes$) will be taken by $C$ to empty the full tank?

$A$ tap can fill the cistern in $8$ hours and another can empty it in $16$ hours. If both the taps are opened simultaneously,the time (in hours) to fill the tank is?

Vedclass Test Series

Exam Paper Generator

Online Exam Module