CoCubes Pipes and Cisterns Question and Answers Quiz-1

Net part of the tank filled in 1 hour = (1/3+1/4-1/6) = 5/12
Therefore, the tank will be full in = 12/5 hours
=2\frac{2}{5} hours

Time by A = 1/10
Time by B= 1/20
Total time =1/10+1/20
= 30/200
= 3/20
= 6.66 hrs.

1/20 +1/30
50/600 = 1/12= 12 minutes

First, it was 3/5 full i.e. (60%)
2 buckets back in it make it 1/2 (50%)
10% means 2 buckets
To empty 100% means 10×2 buckets
=20 buckets

Since we have given that

Number of hours a pipe can fill a tank = 15 hours

Number of hours a pipe can fill if there is a leak in the bottom = 20 hours

Number of hours a pipe would need to empty due to leak be 'x'.

So, According to question, it becomes,

\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{20}

\dfrac{x+15}{15x}=\dfrac{1}{20}

20(x+15)=15x

20x+300=15x

300=15x-20x

300=-5x

x=\dfrac{300}{-5}=-60

Hence, the leak takes 60 hours to empty it.

Suppose the slower pipe alone can fill the tank in x minutes.
Then the faster pipe can fill the tank in x4 minutes.
Part filled by the slower pipe in 1 minute =1/x
Part filled by the faster pipe in 1 minute =4/x
Part filled by both the pipes in 1 minute =1/x+4/x
Given that both the pipes together can fill the tank in 36 minutes.
= Part filled by both the pipes in 1 minute =136
1/x+4/x=1/36
5/x=1/36
x=5×36=180
i.e.,the slower pipe alone can fill the tank in 180 minutes.

tanks*hours*days=tanks*hours*days

20*2*1= x*2*4

X= 5

Pipes A and B can fill the tank in 6 and 5 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/6
part filled by pipe B in 1 hour = 1/5
Pipe C can empty the tank in 18 hours. Therefore,
part emptied by pipe C in 1 hour =1/18
Net part filled by Pipes A,B,C together in 1 hour
1/5+1/6-1/18=28/90=14/45

total part can be filled in 45/14 hours

M1 * D1 = M2 * D2
12 * 30 = M2 * 15
M2 = 24 Men

Let the time taken by pipe j to fill the tank be x minutes
Time is taken by pipe K to fill the tank = x+5 minutes
So, 1/x + 1/(x+5) = 1/6
⇒ x = 10
Thus, time taken by K alone to fill the bucket is 10+5, i.e., 15 minutes