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A man fills a tank in 30mins. A second man fills the same tank in 40mins. And a third man fills it in 60mins. If the three of them fill the tank together:-
i) how long will it take to completely fill the tank?
ii) how long will it take to fill the tank if the third man quits after the tank is 1/4 filled?
The first correct answer gets an automatic employment with Total ;D lol - Just Kidding. But guys try to solve this question.
RATE=TANK VOL/TIME TAKEN ie
R=V/T. ...(1)
FOR D 1ST MAN, R1=V/30...(2)
FOR D 2ND MAN, R2=V/40..,(3)
FOR D 3RD MAN, R3=V/60...(4)
FROM ...(2) V=30R
SUBST. 30R FOR V IN ... (3)
R=30R/40 ie 40=30R/R
40=29R ie R=40/29
i
SUBST. 40/29 FOR R IN ...(3)
40/29= V/40 ie V =1600/29
V= 55.17
R1 = 1.84, R2 = 1.38, R3 = 0.92
ii
THEIR MEAN WORK RATE =
(1.84+1.38+0.92)/3 = 1.38
T = 55.17/1.38 39.98mins
iii
1/4 Of 55.17 TANK = 13.79
T Taken For D 3 to fill 13.79
13.79/1.38 =9.99mins
The new W. Rate for D R1,R2 = 1.61
For the 41.38 unfilled tank ie 55.17-13.79
T =41.38/1.61 = 25.70
Ans =25.70+9.99 =35.69mins
let first man be A
Second man be B
and third man be C
A=1tank=30mins
B=1tank=40mins
C=1tank=60mins
A completes 1/30tank in 1min
B completes 1/40tank in 1min
C complete 1/60tank in 1min
A,B and C complete (1/30 + 1/40 + 1/60)of Tank in 1min
(1/30 + 1/40 + 1/60)= 9/120= 3/40 of Tank in 1min
it will take A,B and C man 1min to fill 3/40 of Tank
it will take 1min * 40/3 to Fill 1 tank
it will take them 13.3mins to fill 1 Tank
b)from above it takes 3.3min for the tank to get to 1/4th filled.
in 3.3mins A will have filled (1/30 * 3.3) of Tank
in 3.3mins B will have filled (1/40 * 3.3) of Tank
and in 3.3mins C will have filled (1/60 * 3.3) of Tank
i.e A=0.11of Tank, B= 0.0825 of Tank and C= 0.055 of Tank.
all men working together in 3.3mins would have completed 0.11 + 0.0825 + 0.055=0.2475 of tank
1-0.2475=0.7525 of tank is left to be filled.
A& B fill rate is 1/30+1/40=7/120 of tank/min
A&B fill rate = 0.0583 of tank/min
recall the vol. left to fill is 0.7525
the time it will take A&B is (0.7525/0.0583) to fill the left vol.
=12.9mins
in all, it takes 3.3+12.9=16.2 to fill the tank.