a2zinterviews

11.	Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern?
	A.  90 min
	B.  100 min
	C.  110 min
	D.  120 min

Solution

Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min.

12.	A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
	A.  4.5 hrs
	B.  5 hrs
	C.  6.5 hrs
	D.  7.2 hrs

Solution

Net part filled in 1 hour = (1/4 - 1/9) = 5/36. Therefore,the cistern will be filled in 36/5 hrs i.e, 7.2 hrs.

13.	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 ?
	A.  15 min
	B.  20 min
	C.  27.5 min
	D.  30 min

Solution

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24. Suppose the tank is filled in x minutes. = 4/8. Then, ‹=›x/2(1/24 + 1/40) = 1 ‹=› x/2×1/15 = 1 x= 30 min.

14.	One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 86 minutes, then the slower pipe alone will be able to fill the tank in
	A.  81 min
	B.  108 min
	C.  144 min
	D.  192 min

Solution

Let the slower pipe alone fill the tank in x minutes. Then, faster pipes will fill it in x/3 minutes. Therefore, 1/x + 3/x = 1/36 ‹=› 4/x = 1/36 ‹=› x= 144 min.

15.	A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?
	A.  3 hrs 15 min
	B.  3 hrs 45 min
	C.  4 hrs
	D.  4 hrs 15 min

Solution

Time taken by one tap to fill half the tank = 3hrs. Part filled by the four taps in 1 hour = (4×1/6) = 2/3. Remaining part = (1 - 1/2) = 1/2. Therefore, ‹=› 2/3 : 1/2 :: 1 : x ‹=› (1/2×1×3/2) ‹=› 3/ 4 hrs i.e 45 mins. So, total time taken = 3 hrs 45 min.