Pipe A can fill a tank in 8 hours and Pipe B can fill it in 6 hours. If both the pipes are opened but after 2 hours pipe A is closed, then the other pipe will fill the tank in
Tank part filled by Pipe A in 1 hour = 1/8
or
Time taken to fill 1/8 part of tank filled A = 1 hour ------------- (1)
Tank part filled by Pipe B in 1 hours = 1/6
or
Time taken to fill 1/6 part of tank filled B = 1 hour ---------(2)
=> Tank Part filled by (A+B) in 1 hour = (1/8 + 1/6)
=> Tank Part filled by (A+B) in 2 hour = 2*(1/8 + 1/6) = 2*(3+4)/24 = 2*7/24 = 7/12
After 2 hours left over portion of tank = (1-7/12) = 5/12
Time taken to fill 1/6 part of tank filled B = 1 hour
so time taken to fill 5/12 part of tank by B = 6 * 5/12 = 5/2 = 2 1/2
=> So it takes 2 1/2 hrs (2hrs 30 min) to fill 5/12 of tank.
Workspace
NA
SHSTTON
36
Solv. Corr.
37
Solv. In. Corr.
73
Attempted
0 M:0 S
Avg. Time
2 / 35
Choose the correct option.
Two pipes A and B can fill a tank in 9 hours and 3 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?
Tank part filled by pipe A in 1 hour =1/9
Tank part filled by pipe B in 1 hour =1/3
Given Pipe A and B are opened alternatively.
So Part filled in every 2 hours =(1/9+1/3)=4/9
Tank Part will be filled in 4 hour =2*4/9=8/9
Remaining part = (1-8/9)=1/9
So next is A turn.
So Pipe A will fill remaining 1/9 part in next 1 hour.
Total Time = (4 hrs + 1 hrs) = 5 hrs.
Workspace
NA
SHSTTON
41
Solv. Corr.
9
Solv. In. Corr.
50
Attempted
0 M:0 S
Avg. Time
3 / 35
Choose the correct option.
A pump takes 8 hours to fill an overhead tank, but due to an open tap in the kitchen, the time taken is 10 hours. In how much time would the kitchen tap empty a full overhead tank?
Pipe A can fill a cistern in 6 hours less than Pipe B. Both the pipes together can fill the cistern in 4 hours. How much time would A take to fill the cistern all by itself?
Let's assume time required by Pipe A to fill the cistern = X hours
So Time required by Pipe B to fill the cistern = (X + 6) hours
? Both Pipes (A+B) can fill cistern in 1 hour = [1/X + 1/(X + 6)]
Given Both pipe fill the cistern in 4 hours
=> [1/X + 1/(X + 6)] = 1/4 => [(X+6) + X]/(X+6)*x = 1/4
4X + 24 + 4X = X2 + 6x
X2 - 2X - 24 = 0
(X-6)(X+4) = 0
=> A can fill cistern in 6 hours.
Workspace
NA
SHSTTON
29
Solv. Corr.
30
Solv. In. Corr.
59
Attempted
0 M:0 S
Avg. Time
5 / 35
Choose the correct option.
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 min, then the slower alone will be able to fill the tank in:
Lets assume time required by slower pipe alone to fill the tank = x minutes.
Then, faster pipe will fill it in x/3 minutes.
=> 1/x+3/x = 1/36
=>4/x = 1/36 => x = 144 min.
Workspace
NA
SHSTTON
17
Solv. Corr.
20
Solv. In. Corr.
37
Attempted
1 M:48 S
Avg. Time
6 / 35
Choose the correct option.
A tap supplies 8 litres of water per minute into a cistern. A leak at the bottom of the cistern can empty the cistern in 10 hours. A full tank with the tap open is emptied by the leak in 15 hours. What is the capacity of the tank?
Tank can be emptied by leak in 1 hour = 1/10
or
Time required to emptied 1/10 part of tank = 1 hour
Given full tank can be emptied by leak = 15 hours
or time need to emptied 1/15 part of tank by leak = 1 hours
so (1/10 - 1/15) part can be filled by tap = 1 hours
=> 1/30 part can be filled by tap = 1 hours
or
Time needed to fill the cistern by tap = 30 hours = 1800 minutes
so Capacity of cistern = 8 * 1800 = 14400 liters
Workspace
NA
SHSTTON
30
Solv. Corr.
26
Solv. In. Corr.
56
Attempted
0 M:0 S
Avg. Time
7 / 35
Choose the correct option.
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Cistern part filled by pipe A in 1 min = 1/20
and by pipe B in 1 min = 1/30
Pipe C empty cistern in 1 min = 1/40 part.
When all pipes are open Cistern part will be filed = (1/20+1/30-1/40) = 7/120
=> Time required to fill the cistern = 120/7 = 17 1/7 min.
Workspace
NA
SHSTTON
22
Solv. Corr.
16
Solv. In. Corr.
38
Attempted
0 M:0 S
Avg. Time
8 / 35
Choose the correct option.
Bucket A has thrice the capacity as bucket B. It takes 80 turns for bucket A to fill the empty drum. How many turns it will take for both the buckets A and B, having each turn together to fill the empty drum?
Lets Assume capacity of bucket A = x
so capacity of bucket B = x/3
Given that it takes 80 turns for bucket A to fill the empty drum.
So capacity of the drum = 80x
Number of turns required if both A and B having each turn together=80x/(x+x/3)=240x/(3x+x)=60
Workspace
NA
SHSTTON
14
Solv. Corr.
17
Solv. In. Corr.
31
Attempted
0 M:0 S
Avg. Time
9 / 35
Choose the correct option.
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Tank part filled by pipe A in 1 minute = 1/60
Tank part filled by pipe B in 1 minute =1/40
So Tank Part filled by both pipes A and B in 1 minute = (1/60+1/40)=5/120=1/24
Lets Assume tanker get filled in x minutes.
Then, to fill the tanker from empty state, B is used for x/2 minutes
and A and B together is used for the rest x/2 minutes.
Pipe A can fill an empty tank in 12 hours. Pipe B can empty it in 36 hours. If at 8 a.m. the pipe A is opened on an empty water tank and pipe B is opended at 9 a.m., 10 a.m. 11 a.m. and 12 p.m. for 15 minutes each, by what time in the evening will the tank be filled?
Tank part filled by Pipe A in 1 hour = 1/12
similarly Tank part emptied by pipe B in 1 hour = 1/36
or Tank part emptied by pipe B in 15 min = 15 * 1/60*36 = 1/144
From 8 a.m. to 9 a.m. tank part filled = 1/12 => 11/12 of the tank is empty
From 9 a.m. to 10 a.m. tank part will be filled = (1/12 + 1/144) = 11/144 => 1 hour 11/144 of the tank gets filled
11/12 part of the tank would take = 11/12 x 144/11 = 12 hours
Total time required is 1 + 12 = 13 hours
=> Tank would be full @ 8 a.m. + 13 = 9 p.m.
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