4 pipes can fill a reservoir in 20,30,40 and 60 hrs respectively. The first was opened at 6 am , second at 7 am, third at 8 am and fourth at 9 am. When will the reservoir be filled up?

• let reservoir will fill in x hours
  (x)/20+(x-1)/30+(x-2)/40+(x-2)/60=1
  x*1/8=17/15
  x = (8*17)/15 = 136/15 = (9+1/15)hr = 9 hr+4 Min
  so resevior will fill 6am + 9 hr+4 Min = 3:04 pm
• 10 years agoHelpfull: Yes(36) No(2)
• 6 am- Empty tank
  7 am = 1/20 full
  8 am= 1/20+(1/20+1/30)
  =1/15 full
  
  9 am= 1/15+(1/20+1/30+1/40)
  =7/40 full
  
  10 am=7/40+(1/20+1/30+1/40+1/60)
  7/40+(1/8) since 4 pipes can fill 1/8 part of the tank in 1 hr
  =3/10 full
  
  so d tank to be filled is 7/10
  
  7/10*8/1= 28/5= 5 hrs 36 mins
  
  
  so the tank ll be filled at 3.36pm
  
  
• 10 years agoHelpfull: Yes(7) No(12)
• let tank will fill in n hours
  n/20+(n-1)/30+(n-2)/40+(n-2)/60=1
  n*1/8=34/30
  n=9.066 hours
  the tank will filled 9+6=15 means 3pm ans...
• 10 years agoHelpfull: Yes(5) No(10)
• 6am-7am--->one in on.amount filled,so=1/20.
  7am-8am--->two in work.amount filled=2*20+1/30.
  8am-9am--->three in work.amount filled=3*20+2/30+1/40.
  9am-10am-->four in work.amount filled=4*20+3/30+2/40+1/60.
  adding them up gives 22/60,that in four hrs.
  in one hr,(1/20)+(1/30)+(1/40)+(1/60) is filled and it equals to 5/8.
  
  so,
  22/60=amount filled in 4hrs,5/8 filled in 1 hr.
  
  22/60+x(5/8)=1,
  x(5/8)=1-22/60=38/60,
  x=(38/60)/(5/8)=1.0133
  
  so totally 4+1.0133 hr=5.0133 hrs.
  
• 10 years agoHelpfull: Yes(3) No(7)
• 1st can fill 1/20 in 1hr
  two can fill 1/12 in 1hr
  three can fill 13/120 in 1 hr
  all four can fill 15/120 in 1 hr
  
  after 9am reservoir left 1-1/20-1/12-13/120
  = 81/120
  and now 81/120 part of reservoir can fill by all pipes in 5.4hr
  
  so tank can fill fully in 8.4 hr
  
• 10 years agoHelpfull: Yes(2) No(3)
• @Sunil Kumar Banjara: the equation would be something like this:
  
  (x)/20+(x-1)/30+(x-2)/40+(x-3)/60=1... you wrote it as (x)/20+(x-1)/30+(x-2)/40+(x-2)/60=1
• 10 years agoHelpfull: Yes(2) No(0)
• @roshan jha is correct it should be (x-3/60) rather than (x-2/60) @sunil kumar banjara....
• 9 years agoHelpfull: Yes(2) No(1)
• Imagine 4 pipes as
  A=20
  B=30
  C=40
  D=60
  total work/LiterS of water (LCM OF ALL)=120
  
  Then A can do 6 work in 1 hour i.e 120/20=6
  similarly B=4 ,ie 120/30
  C=3, ie 120/40
  D=2 ,ie 120/60
  
  image time line as
  6am 7am 8am 9am 10am 11am 12 am 1pm 2pm 3pm
  A's work 6 , 6 6 6 6 6 6 6 6
  B's work 4 4 4 4 4 4 4 4
  C 3 3 3 3 3 3 3
  D 2 2 2 2 2 2
  -------------------------------------------------------------------------------------------------------------------------------------------------
  total 6 10 13 15 15 15 15 15 15...seriesGo on
  Total=6+10+13+15+15+15+15+15+15=119 liters at 3pm
  but LCM earlier=120 liters
  1 hour = 15 liter
  1 minutes=60/15=4
  so the answer will be 3:04pm
• 7 years agoHelpfull: Yes(2) No(0)
• let the time be t hours and the first tap was opened
  in t hours first pipe fills up t*1/20 part....
  4t+3(t-1)+2(t-2)+(t-3)=60
  t=7hrs
  t/20+(t-1)/30+(t-2)/40+(t-3)/60=89/120=1:34pm
• 10 years agoHelpfull: Yes(1) No(2)
• Frm 6 to 9 a hs wrkd 3hrs hence a wrkd 3/20 similarly b=2/30 and c=1/40 so at 9 the wrk remaining =1-3/20-2/30-1/40=87/120
  Aftr 9 all will wrk together a+b+c+d=1/20+1/30+1/40+1/60=15/120
  So time taken aftr 9am=(87/120)×(120/15)=3hrs48min therefore at time (9+3)hr 48 min
• 10 years agoHelpfull: Yes(0) No(2)
• Ans: 3:39 pm
  
  let reservoir will fill in x hrs
  (x)/20 + (x-1)/30 + (x-2)/40 + (x-3)/60=1
  solving we get, x= 136/15 = 9+1/15 hrs = 9 hours and 1/15*60 min = 9 hr+4min
  start at 6am + 9 hr and 4 mins = 3:04pm
• 9 years agoHelpfull: Yes(0) No(0)
• 1st pipe 1 hr work=1/20 ,2nd pipe 1hr work=1/30,3rd pipe 1 hr work=1/40,4th pipe 1 hr work=1/60
  (1st +2nd+3rd+4th) 1 hr work=1/20 + 1/30 + 1/40+1/60=>1/8
  now, work done by every pipe before 9 am =3/20+2/30+1/40+0
  =>29/120
  work left=1-29/120=>91/120
  so, (1st + 2nd +3rd+4th) pipe complete wok=>1 in 8 hr
  so ,(1st + 2nd +3rd+4th) pipe complete wok=>91/120 in (91*8)/120 hr=>6hr 4 min
  so required time=3:04 pm
• 7 years agoHelpfull: Yes(0) No(0)