(cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) SREENIVASA INSTITUTE OF TECHNOLOGY AND MANAGEMENT STUDIES Murukambattu Post, Chittoor–517 127 (A.P) AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY– ANANTAPUR, Course material For Reasoning and Quantitative Aptitude Module Name: PIPES AND CISTERNS (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page1 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) PREREQUISITES: 1. Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet. Outlet: A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet. 2. If a pipe can fill a tank inxhours, then: 1 part filled in 1 hour = . x 3. If a pipe can empty a tank inyhours, then: 1 part emptied in 1 hour = . y 4. If a pipe can fill a tank inxhours and another pipe can empty the full tank inyhours (wherey>x), then on opening both the pipes, then 1 1 the net part filled in 1 hour = - . x y 5. If a pipe can fill a tank inxhours and another pipe can empty the full tank inyhours (wherey>x), then on opening both the pipes, then the net partemptied in 1 hour = 1-1 . 6.Time for filling , (Filling pipe is bigger in size.) F = (e * f)/(e-f) (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page2 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) 7.Time for emptying , (emptying pipe is bigger in size.) E = (f * e)/(f-e) 8.Pipes 'A' & 'B' can fill a tank in f hrs & f hrsrespectively.Another pipe 'C' can empty the 1 2 full tank in 'e'hrs.If the three pipes are opened simultaneously then the tank is filled in F = L/[(L/f ) + (L/f )-(L/e)] 1 2 9.Two taps 'A' & 'B' can fill a tank in 't ' & 't ' hrs respectively.Another pipe 'C' can empty the 1 2 full tank in 'e'hrs.If the tank is full & all the three pipes are opened simultaneously . Then the tank will be emptied in, E = L/[(L/e)-(L/f )-(L/f )] 1 2 10.A filling tap can fill a tank in 'f'hrs.But it takes 'e'hrs longer due to a leak at the bottom.The leak will empty the full tank in , E = [t * t]/[t -t] (f * e) f (f + e) f 11.Capacity of the tank is , F = (f * e)/(e-f) (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page3 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) Solved Examples 1. Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hours respectively.If both the taps are opened together, the tank will be full in ? Ans:6hrs Basic Formula: If A can do a piece of work in x hours and B can do a piece of work in y hours. Then xy A and B together will do the work in hours x(cid:61483) y Answer withExplanation: Time taken by A = 10 hours Time taken by B = 15 hours 15X10 Time taken by A and B = 15(cid:61483)10 15X10 = = 6 hours. 25 2. To fill a cistern, pipes A, B and C take 20 minutes, 15 minute and 12 minutes respectively. Thetime in minutes that the three pipes together will take to fill the cistern is: Ans:5 TCS 2008 Basic Formula: A can do a piece of work in x minutes Bcan do a piece of work in y minutes C can do a piece of work in z minutes Minute’s work of each of the three is 1/x +1/y + 1/z (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page4 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) Answer with Explanation: 1 minutes work of each of the three pipes = 1/20 + 1/15 + 1/12 3(cid:61483)4(cid:61483)5 12 = = 60 60 = 1/5 = 5 minutes 3. Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled? Ans;7 hrs30 mins Basic Formula: Pipe A can fill a tank in x hours and pipe B can fill a tank in y hours and pipe C can empty it in z hours. If all the pipes are operate simultaneously, 1 hours of work of each of the three pipes = 1/x +1/y-1/z Answer with Explanation: 1 minutes work of each of the three pipes = 1/10 + 1/12-1/20 6(cid:61483)5(cid:61485)3 8 = = 60 60 2 = 15 = 15/2 hours = 7 ½ hour = 7 hours 30 minutes. (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page5 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) 4. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If the cistern is full, then the time that the leak will take to empty it is: CAT 2007 Ans:90 hrs Basic Formula: If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be xy filled (empty) in hours x(cid:61485) y Answer with Explanation: Time taken by A = 9 hours Time taken by B = 10 hours 9x10 Time taken by A and B = 10(cid:61485)9 = 90 hours. 5. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 ½ hours to fill the tank. The leak can drain out of all the water of the tank in: Ans:21 hrs Basic Formula: If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled xy (empty) in hours x(cid:61485) y Answer with Explanation: Time taken = 3 hours Time taken = 3 ½ hours 1 3x3 2 Time taken by A and B = 1 3 (cid:61485)3 2 (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page6 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) 7 3x 2 = 7 (cid:61485)3 2 7 3x 2 = 7(cid:61485)6 2 = 21 hours 6. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes. How much further time would it take for B to fill the bucket? WIPRO 2009 Ans 8 min 15 sec Basic Formula: Total work (to fill or empty) = I part + II part =1 Find I st part and subtract it from ‘1’ , then multiply the required section value to find the answer. Answer with Explanation: For 3 minutes (I part) (cid:61670) 1 1 (cid:61686) = 3 (cid:61671) (cid:61483) (cid:61687) (cid:61672)12 15(cid:61688) (cid:61670)15(cid:61483)12(cid:61686) = 3 (cid:61671) (cid:61687) (cid:61672)15X12(cid:61688) (cid:61670) 3 (cid:61686) = 3(cid:61671) (cid:61687)= 9/20 (cid:61672)20(cid:61688) Remaining part = 1-9/20= 11/20 (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page7 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) Tap B fill the bucket in 11 = -15 20 = 33/4 = 8 ¼ hours = 8 hours 15 seconds. 7. A tank can be filled by a tap in 20 minutes and by another tap in 60 mintues. Both taps are kept open for 10 mintues and then the first tap is shut off. After this, the tank will be completely filled in: Ans:20 min Basic Formula: Total work (to fill or empty) = I part + II part =1 Answer with Explanation: For10 minutes (I part) (cid:61670) 1 1 (cid:61686) = 10 (cid:61671) (cid:61483) (cid:61687) (cid:61672)20 60(cid:61688) (cid:61670) 4 (cid:61686) = 10(cid:61671) (cid:61687) (cid:61672)60(cid:61688) = 4/6 = 2/3 Remaining part = 1-( I part) = 1-2/3 = 1/3 The tank will be complete by filled in (B only, after 10 minutes) = 1/3 X 60 = 20 minutes. (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page8 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) 8. If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second pipe to fill the reservoir? ACCENTURE 2008 Ans:30hours Basic Formula: xy Taken unknown value as x and use x(cid:61483) y Answer with Explanation: Let the reservoir be filled by forst pipe in x hours, therefore the second pipe will fill it in (x+10) hours. (cid:61532) 1/x + 1/ x+10 = 1/12 (cid:61670)x(cid:61483)10(cid:61483)x(cid:61686) (cid:61671) (cid:61687) = 1/12 (cid:61671) (cid:61687) (cid:61672) x(x(cid:61483)10) (cid:61688) 12 (10+2x) = x2+10x x2+10x–24x–120 = 0 x2–14x–120= 0 (x-20) (x+6) = 0 (cid:61532) x = 20 (x should nor–ve) (cid:61532) The second pipe can take (x+10) = 20 + 10 = 30 hours, to fill thereservoir. One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened? Ans: 6hours (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page9 (cid:82)(cid:101)(cid:97)(cid:115)(cid:111)(cid:110)(cid:105)(cid:110)(cid:103)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:97)(cid:112)(cid:116)(cid:105)(cid:116)(cid:117)(cid:100)(cid:101) (cid:80)(cid:105)(cid:112)(cid:101)(cid:115)(cid:32)(cid:97)(cid:110)(cid:100)(cid:32)(cid:67)(cid:105)(cid:115)(cid:116)(cid:101)(cid:114)(cid:110)(cid:115) Basic Formula: Pipe A can fill a tank in ‘x’ hours and pipe B can empty it in ‘y’ hours. If both the pipes xy opened together, the tank will be filled in hours. x(cid:61485) y Answer with Explanation: Time taken to fill the tank = 2 hours Time taken to empty the tank = 3 hours 2X3 Time taken to fill the cistern = 3(cid:61485)1 = 6 hours. 9. 12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ? Ans:18 CTS 2007 Basic Formula: Here the tank is same Number of buckets X capacity of bucket = Number of buckets X capacity of bucket Answer with Explanation: The capacity of the tank is same, N X W = N X W 1 1 2 2 N = No. of Buckets W = Capacity of liters in the buckets 1 1 N = No. of Buckets W = Capacity of liters in the buckets 2 2 = 12 X 13.5 = N X9 2 12X13.5 = N = = 54/3 2 9 = N = 18 2 (cid:83)(cid:73)(cid:84)(cid:65)(cid:77)(cid:83) Page10