1. 2 pipes A & B can separately fill a cistern in 60 mins and 75 mins respectively.There is a 3rd pipe in the bottom of the cistern to empty it.If all the 3 pipes are simultaneously then the cistern is full in 50 mins.In how much time the 3rd pipe alone can empty the cistern?

A. 90 mins B. 100 mins C. 110 mins D. 120 mins

Answer Answer: Option B Explanation: Work done by the 3rd pipe in 1 minute
1/50 - (1/60+1/70) = (1/50-3/100) = (-1/100) (- negative means emptying)
3rd pipe alone can empty the cistern in 100 mins

2. A cistern can be filled by a tap in 4 hours while it can be emptied another tab in 7 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

A. 9 hrs B. 9.20 hrs C. 9.30 hrs D. 9.33 hrs

Answer Answer: Option D Explanation: 1/4 - 1/7 = 7-4/28
cistern filled in = 28/3 =9.33 hrs.

3. Pipes 1 and 2 can fill a tank in 18 and 24 hours respectively. Both pipes work simultaneously for sometime after which pipe 1 is turned off. It takes 12 hours in all to fill the tank completely. Find the time for which pipe 1 remained turned on.

A. 9 hours B. 10 hours C. 11 hours D. 12 hours

Answer Answer: Option A Explanation: Let the time for which pipe 1 remained turned on be ‘x’ hours. Hence pipe 1 has worked for ‘x’ hours and pipe 2 has worked for 12 hours.
1/18 (x) + 1/24 (12) = 1
(x/18) + (1/2) = 1 à (x / 18) = (1/2) à x = 9
Pipe 1 remained turned on for 9 hours.

4. Two pipes A & B can fill a tank in 12 mins and 15 mins respectively.If both the taps are opened simultaneously and the tap A is closed after 3 minutes than how much more time will it take to fill the tank by tap B?

A. 7 mins 15 sec B. 7 mins 45 sec C. 8 min 5 sec D. 8 min 15 sec

Answer Answer: Option D Explanation: Part filled in 3 mins = 3 (1/12 + 1/15) = (3*9/16) = 9/20.
Remaining part = (1-9/20) = 11/20
Part filled by B in 1 minute = 1/15
x= (11/20 * 1* 15) = 8 1/4 minute = 8 min 15 sec
Remaining part is filled by B in 8 mins 15 sec

5. 3 taps P, Q and R can fill a tank in 10,20 and 30 minutes respectively.If A is open all the time and Q and R are open for 1 hour each alternatively the tank will be fill in?

A. 7 hrs B. 7 hrs 30 mins C. 8 hrs D. 7 hrs 50 mins

Answer Answer: Option A Explanation: A+B in 1 hour = (1/10)+1/20) = (2+1)/20 = 3/20
A+C in 1 hour =(1/10)+(1/30)=(3+1)/20 = 4/30
In 2 hour => (3/20) + (4/30) = (9+8)/60 = 17/60
part filled in 6 hours = 3*(17/60) = 17/20
Remaining part = 1- (17/20) = (20-17)/20 = 3/20 (filled by A and B) ........ 1 hour
total time taken to fill the tank = 6+1 = 7 hours.