26.  2 pipes can fill a tank in 20 and 24 mins respectively. And a waste pipe can empty 3 gallons per minute.All the 3 pipes working together can fill the tank in 15 minutes.The capacity of the tank is ?


60 gallons
100 gallons
120 gallons
180 gallons


Answer

 Option

Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = ( 1/15 - 11/120) = (- 1/40 (negative sign means emptying) Therefore volume of 1/40 part = 3 gallons. Volume of whole = (3*40) gallons = 120 gallons.

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27.  3 tapes A,B & C can fill a tank in 12,15 and 20 hrs respectively.If A is open all the time and B and C are open for 1 hr each alternately ,the tank shall be full in?


6 hrs
6 2/3 hrs
5 hrs
7 hrs


Answer

 Option

(A+B)'s 1 hour work = (1/12 + 1/15) = 9/60 = 3/20 (A+C)'s 1 hour work = (1/12+1/20) = 8/60 = 2/50 Part filled in 2 hrs = (3/20+2/15) = 17/60 : part filled in 6 hrs = (3*17/60) = 17/20 Remaining part =( 1-17/20) = 3/20 Now it is the turn off A and B and 3/20 part is filled by A & B in 1 hr therefore total time taken to fill the tank = (6+1) hrs = 7 hrs.

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28.  Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full?


4
4 1/2
5
5 1/2


Answer

 Option

A's work in 1 hour = 1/6, B's work in 1 hour = 1/4. (A+B)'s 2 hour's work when opened alternately = (1/6+1/4) = 5/12. (A+B)'s 4 hour's work when opened alternately = 10/12 = 5/6. Remaining part = (1- 5/6) = 1/6. Now, it is A's turn and 1/6 part is filled by A in 1 hour. Therefore total time taken to fill the tank = (4+1) hrs = 5 hrs.

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29.  2 pipes A & B can fill a cistern in 12 mins and 15 mins respectively while a 3'rd pipe C can empty the full tank in 6 mins.A & B are kept open for 5 mins in the beginning then C is also opened. In what time is the cistern emptied?


30 mins
33 mins
37 1/2 mins
45 mins


Answer

 Option

Part filled in 5 minute = 5 (1/12+1/15) = (5*9/60) = 3/4 Part emptied in 1 minute when all the pipes are opened =1/6 - (1/12 + 1/15 ) = ( 1/6-3/20) = 1/60 now 1/60 part is emptied in 1 minute Therefore 3/4 part will be emptied in ( 60*3/4) = 45 mins

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30.  A large tanker can be filled by 2 pipes A & 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 & B fill it together for the half ?


15 minutes
20 minutes
27.5 minutes
30 minutes


Answer

 Option

Part filled by (A+B) in 1 minute = ( 1/60+1/40) = 1/24 suppose the tank is filled in x minutes Then x/2 (1/24 + 1/40) = 1 = x/2 * 1/15 = 1 = x= 30 minutes

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