Pipes and cisterns-Hard test 1

Answer: Option D

Explanation

Let the capacity of the tank be x L

As per the question,

Quantity of water emptied by the leak in 1 h $=\frac{\mathrm{x}}{10}\mathrm{L}$

And to empty 4L in 1h$=\frac{\mathrm{x}}{15}$

Quantity of water filled by the tap in 1 min = 4L

∴1h=4L

As per the question,

$$\begin{gathered} \frac{\mathrm{x}}{10}-\frac{\mathrm{x}}{15}=240 \\ \Rightarrow \frac{3\mathrm{x}-2\mathrm{x}}{30}=240 \\ \Rightarrow \frac{\mathrm{x}}{30}=240 \\ \therefore \mathrm{x}=240\times 30=7200\mathrm{L} \end{gathered}$$

Hence option D is correct.

Answer: Option A

Explanation

Tap A fills 4 buckets in 24 minutes ⇒ $\frac{24}{4}=6 \mathrm{minutes}$

Tap B fills 8 buckets in 1 hour ⇒ $\frac{60}{8}=7.5 \mathrm{minutes}$

Tap C fills 2 bucket in 20 minutes ⇒ $\frac{20}{2}=10 \mathrm{minutes}$

In 2 hours,

Number of buckets filled by tap A ⇒ $\frac{120}{6}=20 \mathrm{buckets}$ 

Number of buckets filled by tap B ⇒ $\frac{120}{7.5}=16 \mathrm{buckets}$ 

Number of buckets filled by tap C ⇒ $\frac{120}{10}=12 \mathrm{buckets}$ 

Total number of buckets filled ⇒  (20 + 16 + 12) = 48 buckets

Total capacity of the tank = Total number of buckets filled X Capacity of each bucket

 ⇒  48 x 5 = 240 L

Hence option A is correct.

Answer: Option B

Explanation

According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is $\left\{ \mathrm{y} \left[1-\frac{\mathrm{t}}{\mathrm{x}}\right] \right\}$ min.

So, $\left\{ 32 \left[1-\frac{18}{24}\right] \right\}=32\times \frac{6}{24}=8 \min$

Hence, the tank will be filled in 8 min both the pipes are opened simultaneously.

Hence option B is correct.

Answer: Option D

Explanation

As per the question,

In 1 minute,

Pipe with 2 cm diameter fills$=\frac{1}{61}$^th of the cistern

Pipe with 1 cm diameter fills$=\frac{1}{61}{\left(\frac{1}{2}\right)}^2=\frac{1}{61}\times \frac{1}{4}$^th of the cistern

Pipe with $1\frac{1}{3}$ cm diameter fills$=\frac{1}{61}\times \frac{1}{4}{\left(\frac{4}{3}\right)}^2=\frac{1}{61}\times \frac{4}{9}$^th of the cistern

∴ In 1 min all the pipes to gether can fill $\frac{1}{61}+\frac{1}{61\times 4}+\frac{4}{61\times 9}=\frac{1}{36}$

Hence in 36 Minutes the complete tank will be filled.

Hence option D is correct.

Answer: Option C

Explanation

According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is $\left\{ \mathrm{y} \left[1-\frac{\mathrm{t}}{\mathrm{x}}\right] \right\}$ hours.

So, $\left\{ 24 \left[1-\frac{16}{32}\right] \right\}=24\times \frac{16}{32}=12 \mathrm{hours}$

Hence, the tank will be filled in 12 hours both the pipes are opened simultaneously.

Hence option C is correct.