Two pipes A and B can fill a cistern in `37 1/2` minutes and 45 minutes respectively . Both pipes are opened . he cistern will be filled in just half an hour , if the pipe B is turned off after :
Answer : Option B
Let B be turned off after `x` minutes . Then
Part filled by (A + B) in `x` min. + part filled by A in (30 - `x`) min. = 1.
`:.` `x(2/75 + 1/45) + (30 - x). 2/75` = 1
`hArr (11x)/(225) + ((60 - 2x))/(75) = 1 hArr 11x + 180 - 6x = 225 hArr x = 9`
Two pipes can fill a tan in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All he three pipes working together can fill the tan in 15 minutes . The capacity of the tank is :
Answer : Option C
Work done by the waste pipe in 1 minute
= `1/15 - (1/20 + 1/24) = (1/15 - 11/120) = - 1/40` [ - ve sign means emptying ]
`:.` Volume of `1/40` part = 3 gallons.
Volume of whole = (3 x 40) gallons = 120 gallons.
A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full , the inlet is opened and due to he leak, the tank is empty in 12 hours. How many litres does the cistern hold ?
Answer : Option D
Work done by the inlet in 1 hour = `(1/8 - 1/12) = 1/24`
Work done by he inlet in 1 min. = `(1/24 xx 1/60) = 1/1440`
`:.` Volume of `1/1440` part of 6 litres.
`:.` Volume of whole = (1440 x 6) litres = 8640 litres.
A booster pump can be used for filling as well as for emptying a tank. The capacity of he tank is 2400` m^3`. The emptying capacity of the tank is 10`m^3` per minute higher than is filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it . What is the filling of the pump ?
Answer : Option A
Let the filling capacity of the pump be `x m^3`/ min.
hen , emptying capacity of the pump = `(x + 10) m^3`/ min.
So , `2400/x - (2400)/((x + 10)) = 8 hArr x^2 + 10x - 3000 = 0`
`hArr (x - 50) (x + 60) = 0 hArr x = 50` [neglecting the - ve value of `x`]
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in :
Answer : Option C
(A + B)'s 1 hour's work = `(1/12 + 1/15) = 9/60 = 3/20`.
(A + C)'s 1 hour's work = `(1/12 + 1/20) = 8/60 = 2/15`.
part filled in 2 hrs. = `(3/20 + 2/15) = 17/60` .
part filled in 6 hrs. = `(3 xx 17/60) = 17/20`.
Remaining part = `(1 - 17/20) = 3/20`.
Now, it is the turn of A and B `3/20` part is filled by A and B in 1 hour.
`:.` Total time taken to fill the tank = (6 +1) hrs. = 7 hrs.