ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A pipe can fill a cistern in 8 hours. Due to an accident, the water flow became half after pouring half of the cistern. How much time will it take to fill the whole cistern?

Solution:
pouring alf of the cistern will take 4 hours.
after that, the flow became half, which means it will take double the time to fill the rest half.
so the next half will be filled in 8 hours.

total time = 4 + 8 = 12 hours.

Question: An ingoing pipe can fill a tank in 5 hours while an outgoing pipe can pour all the water in 15 hours. If both the pipes are open at once, how much time will it take to fill the whole tank?

Solution:
in one hour,
ingoing fillup = 1/5 of the tank
outgoing pour = 1/15 of the tank water
∴ total fillup in one hour = 1/5 - 1/15
= 2/15

total time to fill the tank is = 15/2 = 7.5 hours.

Question: Two pipes that can fill a cistern in 5 hours and 8 hours respectively were used to fill two same-sized cisterns. How much time will it take to fill both the cisterns?

Solution:
in one hour,
1st pipe will fill = 1/5
2nd pipe will fill = 1/8

total fill up
= 1/5 + 1/8
= 13/40

so, the total time to fill two cisterns = 80/13 hours
= 6.15 hours

Question: An ingoing pipe was used to fill a tank. But while using an outgoing pipe that can pour water in 10 hours at the same time, it took 8 hours to fill the tank. The ingoing pipe can fill the tank alone in -

Solution: 
Let,
the ingoing pipe can fill the tank in X hours.
so, total fill-up in one hour = 1/X - 1/10
= (10 - X)/10X
ATQ,
10X/(10 - X) = 8
10X = 80 - 8X
18X = 80
X = 80/18 = 40/9 hours

Question: A pipe can fill 1/6th of a tank in 30 minutes. How much time will it take to fill two tanks?

Solution:
full tank is filled in = (6 × 30) = 180 minutes = 3 hours.

two tanks is filled in = 6 hours

Question: An outgoing pipe pours water at half the amount of an ingoing pipe. After 4 hours of running both pipes, a tank was filled. If the outgoing pipe was closed, how much time would it take to fill the tank with the ingoing pipe?

Solution: 
Let,
ingoing pipe needs X hours,
The outgoing pipe needs 2X hours.

together in one hour, these pipes can fill = 1/X - 1/2X = 1/2X

ATQ,
2X = 4
X = 2
∴ Ingoing pipe will take 2 hours to fill the tank.

Question: Two tanks of the same capacity will be filled by two pipes that have the capacity to fill up a tank in 12 hours and 16 hours respectively. If after filling one tank the pipe is attached to the other one how much time will it take to fill both tanks?

Solution:
the first pipe can fill the first tank in 12 hours.
after that, the pipe will be attached to the second tank.

in 12 hours, the second pipe can fill = 12/16 = 3/4
remaining = 1/4

in one hour, both pipes can fill
= 1/12 + 1/16
= 7/48
so, to fill 1/4 of a tank it will take
= 1/4 × 48/7
= 12/7 hours

total time = 12 + 12/7
= 

Question: After filling half of a tank with an ingoing pipe that can fill the tank in 8 hours, an outgoing pipe was attached to empty the tank in 10 hours. How much time will it take to fill the whole tank?

Solution: 
after 4 hours, the tank will be filled in half.
in one hour,
ingoing can fill = 1/8
outgoing can pour = 1/10
total fill-up in one hour = 1/8 - 1/10
= 1/40
∴ to fill te full tank it will take 40 hours.
so, half of the tank will take 20 hours.

total time to fill the tank from the beginning is = 4 + 20 = 24 hours.

Question: A pipe can fill a cistern in just 4 hours. It took 8 hours to fill the tank after attaching an outgoing pipe to it at the same time. In how much time alone the outgoing pipe can empty the cistern?

Solution:
Let,
the outgoing pipe can empty the cistern in X hours.
total fill-up in one hour
= 1/4 - 1/X
= X - 4/4X

ATQ,
4X/ X - 4 = 8
4X = 8X - 32
X = 8 hours

Question: A pipe was used to fill a cistern in 10 hours but after working for 7 hours it stopped. another pipe that has the capacity to fill the tank in 20 hours was replaced to fill the rest of the tank. How much time will it take to fill the rest of the tank by the second pipe?

Solution: 
in 7 hours,
first pipe fill-up = 7/10
remaining = 3/10

∴ time to fill 3/10 of a tank by the second pipe is
= 3/10 × 20
= 6 hours

Question: A cistern is to be filled by a pipe of capacity 12 hours per cistern. But after every 2 hours, 1/20th of the cistern got empty. How much time will take to fill the full cistern?

Solution:
in two hours total fill up
= 2/12 - 1/20
= 1/6 - 1/20
= 7/60

in one hour = 7/120

total time = 120/7  hours

Question: A pipe can fill 1/8th of a tank in 1 hour. After filling 1/2 of the tank there was a resting period of 2 hours. The rest of the tank was filled simultaneously. What is the average time to fill the 1/8th of the tank?

Solution: 
to fill a full tank it will take 8 hours.
1/2 of the tank = 4 hours.
rest = 2 hours.
rest 1/2 of the tank = 4 hours.
total time = 10 hours.

1/10th of the tank will be filled in 1 hour.
1/8th of the tank in = 1.25 hours = 75 minutes

Question: An outgoing pipe pours water at 10 liters per hour. A cistern of capacity 200 liters was 4/5th full. How much time will the outgoing pipe take to empty the cistern?

Solution: 
total water = 4/5th of 200 liters 
= 160 liters.

time = 160/10 = 16 hours

Question: Some tanks of capacity 720 liters are meant to be filled by three pipes of capacity of loading water at 50 liters, 25 liters, and 15 liters in 10 minutes respectively. In one day they together can fill - 

Solution: 
in 10 minutes total fill-up = (50 + 25 + 15) = 90 liters

in 1 hour = 540 liters.
in 24 hours = (540 × 24) = 12960 liters.

total tank = 12960/720 = 18

Question: Two outgoing pipes, where the first one is double the efficiency of the second one. Both pipes together can empty a tank in just 4 hours. What is the pouring capacity of the first pipe in one hour?

Solution:
Let the second pipe empty the tank in 2X hours.
so, the first pipe can do it in X hours.

total pouring in one hour
= 1/X + 1/2X
= 3/2X

ATQ,
2X/3 = 4
X = 6 hours.

so, the first pipe can pour 1/6 of the tank water in one hour.