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There are two taps to fill a tank and a third to empty it. When the third tap is closed, they can fill the tank in 10 min and 12 min, respectively. If all the three taps be opened, the tank is filled in 15 min. If the first two taps are closed, in approximately what time can the third tap empty the when it is full? 
  • a)
    8 min and 34 second 
  • b)
    9 min and 32 second 
  • c)
    7 min 
  • d)
    6 min 
  • e)
    12 min
Correct answer is option 'A'. Can you explain this answer?
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Solution:

Let the capacity of the tank be 'x'.

Efficiency of the first tap = 1/10 tank/minute

Efficiency of the second tap = 1/12 tank/minute

Efficiency of the third tap = -1/t tank/minute (as it empties the tank)

When the first two taps are open and the third tap is closed, the effective efficiency of both the taps is:

1/10 + 1/12 = 11/60 tank/minute

Time taken to fill the tank = x/(11/60) = 60x/11 minutes

When all three taps are open, the effective efficiency is:

1/10 + 1/12 - 1/t = 1/15

On solving, we get:

t = 8 minutes and 34 seconds

When the first two taps are closed, the efficiency of the third tap is:

-1/t = -1/8.34 tank/minute

Let the time taken by the third tap to empty the tank be 'y' minutes.

Then, the capacity of the tank emptied by the third tap in 1 minute = 1/y tank/minute

As the tank is already full, the time taken by the third tap to empty the tank completely is:

x/(1/y) = xy minutes

On substituting the values, we get:

xy = x/(11/60) - x/(1/15)

Simplifying, we get:

y = 8 minutes and 34 seconds

Hence, option (A) is the correct answer.
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There are two taps to fill a tank and a third to empty it. When the third tap is closed, they can fill the tank in 10 min and 12 min, respectively. If all the three taps be opened, the tank is filled in 15 min. If the first two taps are closed, in approximately what time can the third tap empty the when it is full?a)8 min and 34 secondb)9 min and 32 secondc)7 mind)6 mine)12 minCorrect answer is option 'A'. Can you explain this answer?
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