Q.1.Pipe M and N running together can fill a cistern in 6 minutes. If M takes 5 minutes less than N to fill the cistern, then the time in which N alone can fill the cistern will be
a) 15 min
b) 10 min
c) 30 min
d) 25 min
Sol : Option A Explanation: Let pipe M fills the cistern in x minutes. Therefore, pipe N will fill the cistern in (x+5) minutes. Now, 1/x + 1/(x+5) = 1/6 → x = 10 Thus, the pipe M can fill in 10 minutes, so N can fill in 10+5 =15 minutes.
Q.2. A cistern normally takes 10 hours to be filled by a tap but because of one open outlet pipe, it takes 5 hours more. In how many hours will the outlet pipe will empty a full cistern?
a) 20 hours
b) 24 hours
c) 30 hours
d) None of these
Sol : Option C Explanation: As cistern is filled in 10 hours, therefore in 1 hour, filled part → 1/10th Now, due to outlet pipe, filled part in 1 hour = 1/15th Part of the cistern emptied, due to leakage in 1 hour = 1/10 - 1/15 = 1/30th Therefore the leak will empty the full cistern in 30 hrs.
Q.3. Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?
a) 120 hrs
b) 100 hrs
c) 115 hrs
d) 112 hrs
Sol : Option A Explanation: Cistern filled by both pipes in one hour = 1/12+1/20=2/15th Therefore both pipes filled the cistern in 15/2hrs. Now, due to leakage both pipes filled the cistern in 15/2+30/60=8hrs. Therefore Due to leakage, filled part in one hour = 1/8 Therefore part of cistern emptied, due to leakage in one hour = 2/15-1/8= 1/120th ∴ In 120 hrs, the leak would empty the cistern.
Q.4.Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off,so that the cistern be fill in 24 minutes?
a) 6 min
b) 16 min
c) 10 min
d) 12 min
Sol : Option B Explanation: P can fill the cistern in 36 minutes,so in 1 min, P can fill the cistern = 1/36th part In 24 min, P can fill the cistern = 24/36 = 2/3rd. Remaining part = 1- 2/3 = 1/3rd As Q can fill full cistern in 48 minutes,so it will fill 1/3rd part in 16 minutes.
Q.5.Two pipes A and B can fill a tank in 20 and 16 hours respectively. Pipe B alone is kept open for 1/4 of time and both pipes are kept open for remaining time. In how many hours, the tank will be full?
a) 18 1/3 hrs
b) 20 hrs
c) 10 hrs
d) 12 1/4 hrs
Sol : Option C Explanation: Let the required time be x hours, then ⇒ x/16+3x/80 = 1⇒ x= 11=10 hours.
Q.6.Two taps M and N can separately fill a cistern in 30 and 20 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 5 minutes. After how many minutes was tap M turned-off?
a) 9 min
b) 10 min
c) 12 mi
d) None of these
Sol : Option A Explanation: Let M was turned off after x min. Then, cistern filled by M in x min + cistern filled by N in (x+5) min = 1 ⇒ x/30 + (x+5)/20 = 1 ⇒ 5x+15=60 ⇒ x = 9 min.
Q7.Three fill pipes A, B and C can fill separately a cistern in 12, 16 and 20 minutes respectively. A was opened first. After 2 minute, B was opened and after 2 minutes from the start of B, C was also opened. Find the time when the cistern will be full after opening of C?
a) 3 21/47 min
b) 4 1/2 min
c) 3 9 15/16 min
d) None of these
Sol : Option A Explanation: Let cistern will be full in x min. Then part filled by A in x min + part filled by B in (x-2) min + part filled by C in (x-4) min = 1 ⇒ x/12 + (x-2)/16 + (x-4)/20 = 1 ⇒ 47x - 78 = 240⇒ x = 162/47 = 321/47 min
Q8.A cistern filled in 20 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is thrice as fast as A. How much time will pipe A alone take to fill the tank?
a) 200 hrs
b) 205 hrs
c) 352 hrs
d) Cannot be determined
Sol : Option A Explanation: Suppose pipe A alone takes x hours to fill the tank. Then pipes B and C will take x/3 and x/6 hours respectively to fill the tank. Therefore 1/x + 3/x + 6/x= 1/20 ⇒ 10/x = 1/20 ⇒ x = 200hrs
Q9.Three taps P,Q and R can fill a tank in 10,20 and 30hours respectively. If P is open all the time and Q and R are open for one hour each alternately, then the tank will be full in :
a) 6 hrs
b) 6.5 hrs
c) 7 hrs
d) 7.5 hrs
Sol : Option C Explanation: (P+Q)’s 1 hour’s work = (1/10+1/20) = 3/20 (A+C)’s 1 hour’s work = (1/10+1/30) = 2/15 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 of P and Q and 3/20 part is filled by P and Q in 1 hour. Therefore, Total time taken to fill the tank = (6+1) hrs = 7 hrs
Q10.A tank has a leak which would empty it in 10 hours,a tap is turned on which admits 4 litre a minute into the tank and now it emptied in 12 hours.The capacity of the tank is:
a) 648 litres
b) 1440 litres
c) 1200 litres
d) 1800 litres
Sol : Option B Explanation: Let speed of the bike be x km/hr. Let speed of the electric car be y km/hr ∴ 200/x + 600/y = 10 ∴ 300/x + 500/y = 11 Part filled in 1 hour = (1/10-1/12) = 1/60 Time taken to fill the tank = 60 hours Water filled in 60 hours =4*60*60=1440 litres