A bath tub can be filled by the cold water pipe in 9 minutes and by the hot water pipe in 11.25 minutes. A person left the bathroom after turning on both the pipes simultaneously and returned the moment when the bath tub was full. Finding that the waste pipe had been left open, he closed it. In 3.75 minutes more, the bath tub was full. In what time would the waste pipe empty it? (a) 6.66 minutes (b )66.6 minutes (c) 55.5 minutes (d) 48 minutes (e) none of these
Answers
Solution :-
given that,
→ Time taken by cold water pipe = 9 minutes .
→ Time taken by hot water pipe = 11.25 minutes = 11(1/4) = (45/4) minutes.
So,
→ LCM of 9 and (45/4) = 45 Litre = Let Capacity of Bath Tub.
Than,
→ Efficiency of cold water pipe = (Capacity of bath tub) / (Total time to fill) = 45/9 = 5 Litre/ Min.
→ Efficiency of hot water pipe = (Capacity of bath tub) / (Total time to fill) = 45/(45/4) = 4 Litre/ Min.
Therefore,
→ in 3.75 minutes when waste pipe was closed , both fill = (5 + 4) * 3.75 = 9 * (3(3/4)) = 9 * (15/4) = (135/4) Litre.
we can conclude that, rest was filled before .
Also,
→ cold water pipe and hot water pipe together fill the bath tub in = 45/(4+5) = 5 minutes.
Now, Let us assume that , efficiency of waste pipe is x Litre / Min.
given that, A person left the bathroom after turning on both the pipes simultaneously and returned the moment when the bath tub was full. Finding that the waste pipe had been left open, he closed it.
So, we can conclude that, the person came back after 5 minutes , and in that 5 minutes , cold water pipe, hot water pipe and waste pipe filled Remaining water in the bath tub .
A/q,
→ 5(4 + 5 - x) = Remaining water to be fill..
→ 5(9 - x) = 45 - (135/4)
→ 5(9 - x) = (180 - 135) / 4
→ 5(9 - x) = (45/4)
dividing both sides by 5,
→ 9 - x = 9/4
→ x = 9 - (9/4)
→ x = (36 - 9)/4
→ x = (27/4) Litre / Min.
Hence,
→ Waste Pipe can empty the full bath tub in = (Capacity of Bath tub) / (Efficiency of waste pipe) = 45 /(27/4) = (45*4)/27 = (180/27) = (20/3) = 6.66 Minutes. (Option A) (Ans.)
∴ waste pipe alone can empty the bath tub in 6.66 Minutes.
(Excellent Question .)
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