Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q1.
A tank has leak which would empty the completely filled tank in 10 hours.If the tank is full of water and a tap is opened which admits 4 liters of water per minute in the tank, the leak takes 15 hours to empty the tank. How many liters of water does the tank hold ?
1) 2400 2) 3600
3) 4800 4) 7200
5)None of these
Answer : 7200
Explanation : Let, the capacity of the tank be "X" liters.
According to the problem: 15 x (X/10 - 4 x 60) = X
Or X = 7200 liters
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Q2.
A tank has three drain pipes, the first two pipes A and B operating simultaneously can empty the tank in half the time that of C, third pipe, alone takes to empty it. Pipe A working alone takes half the time taken by pipe B. Together they take to fill the tank in 6 hrs 40 mins. What is time taken for A to empty the tank alone ? 
1) 11hrs 2) 12 hrs
3) 11-1/9hrs 4) 12-1/3hrs
5)None of these
Answer : 11-1/9hrs
Explanation :

Let, C  pipe takes x hrs ,then A  pipe takes x/2 hrs

So, C  pipe takes  =2(x+x/2) =3x hrs

Then, (A+B+C) pipes can do in 1 hr = 1/x + 2/x +1/3x = 10/3x hrs

But given , total time taken by all pipes  = 6 hrs 40 min = 6-2/3 hrs = 20/3 hrs

So, 10/3x hrs = 3/20

Or x =200/9 hrs i.e time taken for pipe B

Therefore, time taken for pipe A = (200/9)/2 = 100/9 = 11-1/9hrs

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Q3.
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. In how many hours the pipe C alone can fill the tank ?
1) 8hrs 2) 10hrs
3) 12hrs 4) 14hrs
5)None of these
Answer : 14hrs
Explanation :

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Q4.
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately ?
1) 2 hour 2) 3 hour
3) 4 hour 4) 6 hour
5)None of these
Answer : 6 hour
Explanation :
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Q5.
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. What is the capacity of the tank ?
1) 80 gallons 2) 120 gallons
3) 140 gallons 4) 160 gallons
5)None of these
Answer : 120 gallons
Explanation :
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Q6.
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in :
1) 81 min. 2) 108 min.
3) 144 min. 4) 164 min.
5)None of thesae
Answer : 144 min.
Explanation : Let, the slower pipe alone will fill the tank in x minutes.
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Q7.
Two Pipes A and B working together can fill a cistern in 6 min. If B takes 5 min more than A to fill the cistern, then the times in which A and B will fill the cistern separately will be respectively ?
1) 15 min., 20 min 2) 15 min, 10 min
3) 10 min, 15 min 4) 25 min, 20 min
5)None of these
Answer : 10 min, 15 min
Explanation :
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Q8.
Two pipes can fill a tank in 10 hour and 12 hours respectively while the third can empty it in 20 hours. If all the pipes are opened together,in how many hrs the tank will be filled ? 
1) 7.5 hours 2) 8 hours
3) 8.5 hours 4) 12 hours
5)None of these
Answer : 7.5 hours
Explanation : Work done by all the tanks working together in 1 hour.

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Q9.
A cistern is filled in 5 hrs and it takes 6 hrs when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it ?
1) 12 hour 2) 15 hour
3) 24 hour 4) 30 hour
5)None of these
Answer : 30 hour
Explanation :
Let, the leak empties the tank in x hours.
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Q10.
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. What is time for the  first pipe to fill up the tank alone ?
1) 10hrs 2) 12hrs
3) 15hrs 4) 18hrs
5)None of these
Answer : 15hrs
Explanation :
Let, the first pipe can alone takes x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively . 
So,(1/x) + (1/x-5) = 1/x-9. 
Solving,we get x =15
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