# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. Three pipes $A$, $B$ and $C$ are connected to a tank. These pipes can fill the tank separately in 5 hr, 10 hr and 15hr respectively. When all the three pipes were opened simultaneously, it was observed that pipes $A$ and $B$ were supplying water at $\left(\dfrac{3}{4}\right)^{th}$    of their normal rates for the 1st hour after which they supplied water at normal rate. Pipe $C$ supplied water at  $\left(\dfrac{2}{3}\right)^{th}$of its normal rate for 1st 2 hours, after which it supplied at its normal rate. In how much time, tank would be filled?
 ✖ A. 1.05 hr ✖ B. 2.05 hr ✔ C. 3.05 hr ✖ D. None of these

Solution:
Option(C) is correct

The part of the tank filled by $A$ and $B$ in first two hour

$\Rightarrow \dfrac{3}{4}\times \left(\dfrac{1}{5}+\dfrac{1}{10}\right)+\left(\dfrac{1}{5}+\dfrac{1}{10}\right)$

The part of tank filled by $C$ in first two hours = $2\times \dfrac{2}{3}\times \dfrac{1}{15}$

Remaining part = $\dfrac{139}{360}$

In 1 hour, all the three pipes together will fill = $\dfrac{11}{30}$

Hence, the time taken to fill the remaining tank = $\dfrac{139}{360}\times \dfrac{30}{11}$= 1.0530 hour

Thus, the total time taken to fill the remaining tank = 3.05 hour.

## (8) Comment(s)

Priya
()

how did 139/360 come ?

Vineet
()

Pipe P1 can fill a cistern in 40 hours. Pipe P2 can empty the same completely filled cistern in 60 hours. If in every 3 hours P1 runs in the first two hours and P2 runs in the last hour, then how long will it take to fill the same half filled cistern?

Options are:

1 43 hours 20 minutes

2 45 hours 40 minutes

3 47 hours 20 minutes

4 45 hours

5 43 hours

Manohar Tangi
()

45 hours....................?

Khushboo
()

43 hrs 20 mins..................

Dan
()

Why can't we use the following way to solve this problem?

In 1st hour the performance of the 3 pipes will be following:

Pipe A = $5*0.75=3.75 hrs$

Pipe B = $10*0.75=7.5 hrs$

Pipe C = $15* 2/3 = 10 hrs$

So for 1st hour we get the following:

$1*(1/3.75+1/7.5+1/10)=x$

$x=0.5$

So in 1 hour half of tank was filled

For the following another hour we have the following:

Pipe A = $5 hrs$

Pipe B = $10 hrs$

Pipe C = $10 hrs$

Amount of tank filled for another hour is :

$1*(1/5+1/10+1/10)=x$

$x=0.4$

For 1st 2 hours amount of tank filled is 0.5+0.4=0.9

The 0.1 amount of tank will be filled in:

$x*(1/5+1/10+1/15)=0.1$

$x= 16 mins$

So the tank will be filled in 1+1+0.25= 2.25 hours

Parag
()

its wrong. the answer has to be above 2.5hrs

Shaibal
()

Is it correct that all the three pipes together will fill $= \dfrac{11}{30}$?

Since according to my calculation all the three pipes together will fill in one hour will be $\dfrac{221}{360 \times 2}$

Hamza
()

In one hour the three pipes will fill,

$\left(\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{15}\right)=\dfrac{11}{30}.$

I guess you are making some mistake somewhere.

If you show me the steps of your calculation, maybe I can be of help.