Latest Elitmus Aptitude Question SOLUTION: Pipes A and B can fill a cistern in 20 min and 30 min and C can empty it in 15 min. If the three are kept open successively for 1 min each in the order how soon will the cistern be

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(#M40033044) ELITMUS Numerical Ability question Pipes and cistern Keep an EYE

Pipes A and B can fill a cistern in 20 min and 30 min and C can empty it in 15 min. If the three are kept open successively for 1 min each in the order how soon will the cistern be filled?

Asked In Elitmus (10 years ago)

Unsolved Read Solution (26)

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Shankar  (10 years ago)

A alone fill the cictern in 1 min 1/20 part of cictern.
B alone fill the cictern in 1 min 1/30 part of citern
and c empty the cictern in 1 min 1/15.

now now they kept opne successively

so in 2 min A and B fill tank (1/20+1/30) = 1/12

now in next 3rd min tank will be empty (1/12-1/15)= 1/60

so 1/60 part filled in 3 min

then full tank filled in 3*60 = 180 min

Is this solution Helpfull? Yes (61) | No (22)  

Leelanand Kumar Yalla  (10 years ago)

167 minutes or 2 hours and 47 minutes... A can Fill the tank in one minute 1/20th part. where as B can fill the tank in one minute 1/30. where as C empties the tank in one minute is 1/15; So these are consequently 'on' for every one minute. therefore 1/20+1/30-1/15;
(3+2-4)/60; here total we have to get 60 to fill the tank so in first minute 3 adds and inn second minute 2 adds and in third minute -4 adds so for every 3 minutes only 1 part is filled like the way for 165 minutes 55th part has filled, next 1 minute 3 parts and next 1 minute 2 parts. so totally 167 minutes. it will fill the tank..

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kaushal jaiswal  (10 years ago)

A alone fill the cictern in 1 min 1/20 part of cictern.
B alone fill the cictern in 1 min 1/30 part of citern
and c empty the cictern in 1 min 1/15.
so, in 1 min cictern fill (1/20+1/30-1/15)part of cictern
i.e; 1/60 part of cictern filled by A B C in 1 min
so to fill whole cictern it will taken time 60 min.
so, ans is 60 min.

Is this solution Helpfull? Yes (18) | No (21)  

manivikas  (10 years ago)

Here is some confusion that either they are open all at a time or one after another ... which takes u to two diiff answers...
in my view that is second case ( one after another ) so ans 167..

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PRAVIN KUMAR  (10 years ago)

Ans will be 167 min. This is the right answer.

Is this solution Helpfull? Yes (4) | No   

ashish bharti  (10 years ago)

one day work of three in 3 day time=1/20+1/30-1/15
=1/60
Hence total 60*3=180 min required.

Is this solution Helpfull? Yes (3) | No (11)  

Amit Kumar Shrivastava  (10 years ago)

The % of Work Done By A=100/20=5% in one Minute.
The % of Work Done By B=100/30=3.33% in one Minute.
The % of Work Done By C=100/15=6.67% in one Minute.
Hence % of Work Done By A+B+(-C) in one Minute=5+3.33-6.67=1.67%
How Soon Cistern be filled =100/1.66=59.88% ~60 Day Ans.

Is this solution Helpfull? Yes (3) | No (8)  

pranay  (9 years ago)

suppose total work done is 60 unit
then A will do 3 unit per minute
B will do 2 unit per minute
C will do 4 unit per minute
so in 3 minute total unit done is (3 + 2) - 4 = 1 unit
57 unit done in (57 * 3) minute = 177 minute
now remaining (60 - 57) = 3 unit done by A in 1 minute
total time is (177 + 1) minute = 178 minute

Is this solution Helpfull? Yes (3) | No (3)  

SHASHIKANT  (10 years ago)

ans=50min.
A alone fill the cictern in 1 min 1/20 means 5% part of cictern.
B alone fill the cictern in 1 min 1/30 means 3.33% part of citern
and c empty the cictern in 1 min 1/15 means 6.33%.
so, in 1 min cictern fill (5+3.33-6.33)%=2%part of cictern
i.e; 2% part of cictern filled by A B C in 1 min
so to fill whole(100%) cictern it will taken time 50 min.
so, ans is 50min.

Is this solution Helpfull? Yes (1) | No (8)  

Anurag Yadav  (10 years ago)

Since each tank is opened in successful intervals therefore in 3 min total tank filled will be 1/20 +1/30-1/15=1/60
So total time would be 60×3=180 min or 3 hrs

Is this solution Helpfull? Yes (1) | No (5)  

raj  (9 years ago)

167 minutes or 2 hours and 47 minutes.. is the right answer

Is this solution Helpfull? Yes (1) | No   

MANPREET SINGH  (10 years ago)

A alone fill the cistern in 1 min 1/20 part of cistern.
B alone fill the cistern in 1 min 1/30 part of cistern
and c empty the cistern in 1 min 1/15.
so, in 3 min cistern filled would be (1/20+1/30-1/15)part of cistern=1/60
in 55 min cistern filled would be 55/60 part of cistern
in 57 min cistern filled would be 55/60+1/20+1/30 part of cistern=1
so in 57 min cistern will fully filled

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deepak  (10 years ago)

efficiency of a=5%,b=3.33%,c=-6.66% therefore in 3 min 5+3.33-6.66=1.67 we need to fill 100% therefore 1.69*59 ans is 59 or approx 60

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Kedarnath  (10 years ago)

A fills 1/20 part
B fills 1/30 part
C empties 1/15 part .. all in one min..
As they r opened successively after 1 min ..
1/60 part will be filled in first 3 min (1/20+1/30-1/15)
Now.. from the 4rth min all the three are open ..so for 1 min 1/60 will be filled then 59/60 will be filled in 59 minutes
SO total time taken is 59+3 = 62 min...

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Pratap K Desai  (10 years ago)

in first min = tank filled 1/20
in sec min = 1/20 + 1/30
in 3rd min 1/20 + 1/30 - 1/15
after 3rd min tank filled will be 3/20
then time taken to fill tank = 20/3 * 3
20 mins

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Varshika  (9 years ago)

ans is 172

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Vandit Jain  (9 years ago)

3 hours or 180 min

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AMIT KUMAR  (9 years ago)

A fills in 1 min 1/20 part
B fills in 1 min 1/30 part
c empty in 1 min 1/15 part
so 1/20+1/30-1/15=1/60
each pipe takes 1 min successively. So 3*60=180min
ans is 180 min.

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mratyunjay kaushik  (9 years ago)

179
..............
A alone fill the cictern in 1 min 1/20 part of cictern.
B alone fill the cictern in 1 min 1/30 part of citern
and c empty the cictern in 1 min 1/15.

now now they kept opne successively

so in 2 min A and B fill tank (1/20+1/30) = 1/12

now in next 3rd min tank will be empty (1/12-1/15)= 1/60

so 1/60 part filled in 3 min

then full tank filled in 3*60 = 180 min

but on 180th min tank would be empty means that it would have been filled in 179th min

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Ameena  (9 years ago)

total work=60 units
a work =3units
b work=2units
c work=4 units
for first min tank filled=3units(only a open)
for second min tank filled =3+2=5(a b open)
assume from 3 min onwards tank took x min to fill
and tank filled for 3 min=3+2-4=1(a b c open)
now 3(1st min)+5(second min)+x*1(process repeated from 3rd min)=60(total units)
8+x=60
x=52
so total time=2min+x=2+52=54min

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NIKHIL RANAJN  (9 years ago)

167 is the correct ans, after 165 mins we have 15/180 left .after pipe a 2/60 left .hence that amount can be filled by pipe b in 1 min

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karthik  (8 years ago)

167 minutes is the right answer 100% sure.

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vijeta kumari  (8 years ago)

This is like the question where a man takes 3 steps forward and one backward. So the pipes are opened successively with each being open for 1 min. then
Work done by A in 1 min =1/20
Work done by B in 1 min=1/30
Work done by C in 1min= -1/15
So usually the time taken to do 1 work comes up to 180 minutes as : Work done by 3 in 3 minutes = 1/60
so 1/60 work done takes 3 minutes , 1 work takes 180 minutes, simple unitary method, However at 180th minutes the tank is once filled more than the required amount and then emptied, so at 179th minute the tank is filled 16/17th part of which C empties 1/15 to get 1 filled tank but, the tank cant be filled over its capacity , hence we need to find the time when it was actually filled, so 1/15th is the extra amount that was filled.
in 1 min B alone cannot fill 1/15th tank as work done by B in 1 min is 1/30. So A too had a part in filling extra water. B filled 1/30 of 1/15 so remaining is 1/30 now A takes more 1/3 minutes to fill this much water.now 180-1=179, for c not emptying the tank. 179-1 for extra water not required but poured by B.
178-1/3(of a minute)= 178 2/3 minutes taken to fill the tank.

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Vikash kumar  (8 years ago)

correct answer =180

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allok  (7 years ago)

Pipe A will fill 20% in one minute.pipe B will fill 3.33% in one minute and pipe C will empty 6.66% in one minute ( by percentage method simply).
Now according to given order the starting 3 min will be 5% in one min+3.33 in 2nd minute -6.66 in 3rd minute successively 5+3.33-6.66=1.67)and so on till we get 100 % or the cistern will be filled completely. So in first 2 minute we add up the % because the are filling the cistern but in 3rd minute we subtract 6.66 because it empties the cistern and this continues. As the cistern will full we must stop there. So u will see that after 164 min u will get 91.67% cistern is filled so then only 2 more minute needed to get 100% i,e 91.67% +5%+3.33=100 that gives 167 approx.

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khushi Pokharna  (3 years ago)

In one minute pipe A can fill 1/20

In one minute Pipe B can fill 1/30

In one minute pipe C can empty 1/15

So in one minute 1/20+1/30–1/15 of tank will be full.

3/60+2/60–4/60=1/60 will be full.

So it takes 60 minutes to fill the tank if all the pipes are opened together.

Now the question is if pipe A is opened for a minute and closed and pipe B is opened for a minute and closed and pipe C is opened and closed for a minute successfully

Then it takes three minutes to what will happen normally in one minute if all pipes are open.

The tank will be full by 3*60 =180 minutes. But we need to calculate logically

In 165 minutes it will be full upto 55/60

In 166 minutes it will be 55/60 +1/20=58/60

In 167 minutes it will be 58/60+1/30=60/60.

So the tank will be full by 167 minutes and again we don't have to open the pipe C.

So the tank will be full in 167 minutes and the process of opening and closing has to stop.

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