Question Detail

A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?

20 hours
19 hours
90 hours
80 hours

Answer: Option C

Explanation:

Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10

Work done by leak in 1 hour

$\begin{aligned} = \frac{1}{9} - \frac{1}{10} \\ = \frac{1}{90} \end{aligned}$

We used subtraction as it is getting empty.

So total time to empty the cistern is 90 hours

1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

10 mins
12 mins
15 mins
20 mins

Answer: Option B

Explanation:

In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as

Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30

Part filled by (A+B) in 1 min = 1/20 + 1/30
= 1/12

So both pipes can fill the tank in 12 mins.

2. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?

10 hours
13 hours
17 hours
21 hours

Answer: Option D

Explanation:

We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as

Work done for 1 hour without leak = 1/3
Work done with leak =

$\begin{aligned} 3\frac{1}{2} = \frac{7}{2} \\ \text{Work done with leak in 1 hr= }\frac{2}{7} \\ \text{Work done by leak in 1 hr }\\ = \frac{1}{3} - \frac{2}{7} = \frac{1}{21} \end{aligned}$

So tank will be empty by the leak in 21 hours.

3. Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.

$\begin{aligned} 3\frac{9}{5} \end{aligned}$
$\begin{aligned} 3\frac{9}{17} \end{aligned}$
$\begin{aligned} 3\frac{7}{5} \end{aligned}$
$\begin{aligned} 3\frac{7}{17} \end{aligned}$

Answer: Option B

Explanation:

Net part filled in 1 hour =

$\begin{aligned} \left(\frac{1}{5}+\frac{1}{6}-\frac{1}{12}\right) \\ = \frac{17}{60} hrs \\ = 3\frac{9}{17} \end{aligned}$

4. A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.

2 hours 30 mins
2 hours 45 mins
3 hours 30 mins
3 hours 45 mins

Answer: Option D

Explanation:

Half tank will be filled in 3 hours
Lets calculate remaining half,

Part filled by the four taps in 1 hour = 4*(1/6) = 2/3

Remaining part after 1/2 filled = 1-1/2 = 1/2

$\begin{aligned} \frac{2}{3}:\frac{1}{2}::1:X \\ => X = \left( \frac{1}{2}*1*{3}{2} \right) \\ => X = \frac{3}{4} hrs = 45 \text{ mins} \\ \end{aligned}$
Total time = 3 hours + 45 mins = 3 hours 45 mins

5. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

6 min to empty
7 min to full
6 min to full
7 min to empty

Answer: Option A

Explanation:

There are two important points to learn in this type of question,
First, if both will open then tank will be empty first.

Second most important thing is,
If we are calculating filling of tank then we will subtract as (filling-empting)

If we are calculating empting of thank then we will subtract as (empting-filling)

So lets come on the question now,

Part to emptied 2/5

Part emptied in 1 minute =

$\begin{aligned} \frac{1}{6} - \frac{1}{10} \\ = \frac{1}{15} \\ => \frac{1}{15}:\frac{2}{5}::1:x \\ => \frac{2}{5}*15 = 6 mins \end{aligned}$

Question Detail

A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?

1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

2. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?

3. Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.

4. A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.

5. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

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Question Detail

A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?

1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

2. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?

3. Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.

4. A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.

5. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

Thanks ! Your comment will be approved shortly !

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