Pipes and cisterns-Basic test 1

Answer: Option C

Explanation

According to the formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then full tank will be filled in $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

So,

$$\begin{gathered} \frac{5\times 6\times 12}{\left(5\times 12\right)+\left(6\times 13\right)-\left(5\times 6\right)} \\ =\frac{360}{72+60-30}=\frac{360}{102}=3\frac{9}{17} \mathrm{hours} \end{gathered}$$

The tank will be filled in $3\frac{9}{17}$ hours when all the pipes are opened simultaneously.

Hence option C is correct

Answer: Option C

Explanation

According to the formula, if a pipe can comletely empty a tank in x hours, then the portion emptied in 1 hour is $\frac{1}{x}$.

outlet pipe can empty the tank in 39 min.

$\frac{1}{39}$^th part of the tank will be emptied by outlet pipe  in 1 min.

Hence option C is correct

Answer: Option A

Explanation

Time taken to empty full tank is 3 hours

otime taken to empty $\frac{2}{3}$ part can be calculated as follows,

$\frac{2}{3}\times 3=2 \mathrm{hours}$

Hence option A is correct

Answer: Option A

Explanation

According to the formula, if a pipe can comletely fill a tank in x hours, then the portion filled in 1 hour is $\frac{1}{x}$.

As Pipe completely fills the tank in 6 hours.

$\frac{1}{6}$^th part of the tank will be filled by pipe A  in 1 hour.

Hence option A is correct

Answer: Option A

Explanation

According to the formula, if a pipe fills $\frac{1}{\mathrm{x}}$ part of tank in 1 hour, then it takes x hours to fully fill the tank.

$$\begin{gathered} \frac{1}{\mathrm{x}}=\frac{1}{9} \\ \therefore \mathrm{x}=9 \end{gathered}$$

The pipe will take 9 hours to fill the tank.

 Hence option A is correct