Pipe A fills a tank of capacity 700 liters at the rate of 40

Question

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

A) 42 minutes
B) 14 minutes
C) 39 minutes
D) 40 minutes 20 seconds
E) None of these

Show Answer

Official Answer

D

A) 42 minutes
B) 14 minutes
C) 39 minutes
D) 40 minutes 20 seconds 
E) None of these

Bunuel · Accepted Answer

In three minutes net gain is 40+30-20=50 liters;

After 13 cycles (13*3=39 minutes) net gain will be 13*50=650 liters.

Then in 1 minute pipe A will add 40 liters, 10 liters to be filled;

Then to fill 10 liters pipe B will need 10/30=1/3 min.

So total time  39+1+\frac{1}{3}=40\frac{1}{3}  min.

gurpreetsingh · Answer

In one cycle they fill 40+30-20 = 50 liters

700 = 50*n => n = 14
here n = number of cycles.

total time = 14*3 = 42 as in one cycle there are 3 minutes.

thus 42 minutes....whats the OA?

gurpreetsingh · Answer

Yes, right....

Thanks

bibha · Answer

How do you get that cycle = 13???

janani · Answer

@ bibha

divide 700/50... u get 14 cycles.
but u know that before 20 
then take away the last cycle. so u have 13 cycles (39 mins), where the tank is 650 ls full.
let's take the 14th cycle. the first minute, the tank gets to 650 + 40 = 690ls.
there's only 10 ls left to fill the tank.
the second step of the cycle is pipe B that fills 30 ls in 1 minute. since we only need 10 ls, we only need 1/3rd of a minute.

so we have 13 cycles plus 1 min of pipe A and 1/3rd minute of pipe B.

samheeta · Answer

I still dont get it.... i mean I understand everything but the logic as to why we should NOT consider 14 cycles as we have already done the filling in and filling out calculations.

Zarrolou · Answer

The sequence of the events is:
Pipe A adds  40  liters/m
Pipe B adds  30  liters/m
Pipe C subtracts  20  liters/m
=NET  +50

When you have done 13 circles in 40 minutes, there are 650 liters and 50 to go.
Now the squence repeats
Pipe A adds  40  liters/m----50-40=10 liters to go and 1 minute more added
Pipe B adds  30  liters/m----so 10 liters will be filled in  \frac{1}{3}  of a minute
STOP
Pipe C subtracts 20 liters/m

Tot time  40  minutes and  \frac{1}{3}

Kinshook · Answer

aiming4mba 
Given: Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute.

Asked: If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
Tank filling progress = (40 + 30 - 20) + (40 + 30 - 20) + ...... 
= 50 + 50 + 50 + ...... 13 times + 40 + 30/3

Since 700 = 50*14

Tank will be full in minutes = (3*13 + 1) minutes 20 seconds = 40 minutes 20 seconds

IMO D

8Harshitsharma · Answer

TECHNICALLY, the tank will be full at both 42 minutes and 40 minutes 20 seconds - HENCE THE QUESTION STEM IS AMBIGUOUS and CHOICE A and CHOICE D BOTH ARE CORRECT.

QS should lead us to the right answer by saying something like "when will the tank be FIRST full" OR "what is the EARLIEST TIME the tank will be full"

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Pipe A fills a tank of capacity 700 liters at the rate of 40

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