31. 2 pipes A & B can fill a tank in 15 hrs and 20 hrs respectively while a 3'rd pipe C can empty the full tank in 25 hrs. All the 3 pipes are opened in the beginning. After 10 hrs C is closed. In how much time will the tank be full?

A. 12 hrs B. 13 hrs C. 16 hrs D. 18 hrs

Answer Answer: Option A Explanation: Part filled in 10 hrs= 10 ( 1/15 + 1/20 - 1/25 ) = 23/30
Remaining part = (1-23/30) = 7/30
(A+B)'s 1 hrs work = (1/15 + 1/20) = 7/60
x= (7/30 * 1* 60/7) = 2 hrs
Hence the tank will be full in (10+2) hrs = 12 hrs.

32. 2 pipes A & B can fill a tank in 15 minutes and 20 minutes respectively.Both the pipes are opened together but after 4 minutes pipe A is turned off.What is the total time required to fill the tank?

A. 10 mins 20 sec B. 11 mins 45 sec C. 12 mins 30 sec D. 14 mins 40 sec

Answer Answer: Option D Explanation: Part filled in 4 mins = 4(1/15 + 1/20) = 7/15
Remaining part = ( 1-7/15) = 8/15
Part filled by B in 1 minute = 1/20
X = (8/15*1*20) = 10 2/3 min.=10 min 40 sec.
The tank will be full in( 4 min + 10 min 40 sec) = 14 min.40 sec.

33. 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

34. A tank is filled by 3 pipes with uniform flow.The first 2 pipes operating simultaneously fill the tank in the same time during which the tank is filled by the 3'rd pipe alone.The 2'nd pipe fills the tank 5 hrs faster than the 1'st pipe and 4 hrs slower than the 3'rd pipe.The time required by the first pipe is?

A. 6 hrs B. 10 hrs C. 15 HRS D. 30 HRS

Answer Answer: Option C Explanation: SUPPOSE 1'st pipe alone takes x hrs.To fill the tank than 2'nd & 3'rd pipes will take (x-5) & ( x-9) hrs respectively to fill the tank.
therefore 1/x+1/(x-5) = 1/(x-9) = x-5 +x / x(x-5) = 1/(x-9)
(2x-5) (x-9) =x(x-5) = x (x-5) = x^2 -18x +45 =0
(x-15) (x-3) = 0 =
x=15

35. A tank is filled in 5 hours by three pipes A,B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank ?

A. 20 hrs B. 25 hrs C. 35 hrs D. None of these

Answer Answer: Option C Explanation: Suppose pipe A alone takes x hrs to fill the tank then
Pipes B and C will take x/2 and x/4 hrs respectively to fill the tank
1/x+2/x+4/x = 1/5 = 7/x = 1/5 = 35 hrs