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Tank and tap problem

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Tank and tap problem

by knight247 » Tue Jul 12, 2011 10:43 am
A tank is fitted with an inlet which takes 1 hour to completely fill the empty tank. The tap was turned on when the tank was empty. When the tank was half filled , it developed a leak and as a result it took totally 65 minutes to fill the tank. As soon as the tank got filled completely, the tap was turned off but the leakage continued. How long will it take for the leakage to empty the tank completely.

Sorry but don't have answer options on this one. Also don't have an OA. Would appreciate if the
answer can be explained step by step in detail...thanks
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by GMATGuruNY » Tue Jul 12, 2011 12:22 pm
knight247 wrote:A tank is fitted with an inlet which takes 1 hour to completely fill the empty tank. The tap was turned on when the tank was empty. When the tank was half filled , it developed a leak and as a result it took totally 65 minutes to fill the tank. As soon as the tank got filled completely, the tap was turned off but the leakage continued. How long will it take for the leakage to empty the tank completely.

Sorry but don't have answer options on this one. Also don't have an OA. Would appreciate if the
answer can be explained step by step in detail...thanks
Let tank = 60 units.
Rate of tap = w/t = 60/60 = 1 unit per minute.
Time for tap to fill half the tank = w/r = 30/1 = 30 minutes.
Since the total time is 65, time to fill the remaining half of the tank is 65-30 = 35 minutes.
Thus, rate with leak = w/t = 30/35 = 6/7 units per minute.
Rate of leak = Rate of tap alone - Rate of tap with leak = 1- 6/7 = 1/7 units per minute.
Time for leak to empty the full tank = w/r = 60/(1/7) = 420 minutes = 7 hours.
Last edited by GMATGuruNY on Tue Jul 12, 2011 3:54 pm, edited 1 time in total.
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by Anurag@Gurome » Tue Jul 12, 2011 12:29 pm
knight247 wrote:A tank is fitted with an inlet which takes 1 hour to completely fill the empty tank. The tap was turned on when the tank was empty. When the tank was half filled , it developed a leak and as a result it took totally 65 minutes to fill the tank. As soon as the tank got filled completely, the tap was turned off but the leakage continued. How long will it take for the leakage to empty the tank completely.
Let us assume that the capacity of the tank is 60 L.

Hence,
  • Only tap : Entry of 60 L per 60 min = 1 L/min
    Tap + Leak : Entry of 30 L per 35 min = 30/35 L/min = 6/7 L/min
Therefore, only leak : Exit of (1 - 6/7) = 1/7 L/min

Thus 1/7 L leaves the tank through the leakage in 1 minute.
--> 60 L leaves the tank through the leakage in 60*7 minutes = 7 hours

Thus, it will take 7 hours for the leakage to empty the tank completely.
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by kevincanspain » Tue Jul 12, 2011 1:59 pm
knight247 wrote:A tank is fitted with an inlet which takes 1 hour to completely fill the empty tank. The tap was turned on when the tank was empty. When the tank was half filled , it developed a leak and as a result it took totally 65 minutes to fill the tank. As soon as the tank got filled completely, the tap was turned off but the leakage continued. How long will it take for the leakage to empty the tank completely.

Sorry but don't have answer options on this one. Also don't have an OA. Would appreciate if the
answer can be explained step by step in detail...thanks
The second half of the tank took 35 minutes to fill when it should have taken only 30. These extra 5 minutes of flow represent 1/12 of the tank. Thus in 35 minutes the leak empties 1/12 on the tank, so the leak would empty the entire tank in 12 x 35 minutes = 35/5 hours
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by jonathan123456 » Tue Jul 12, 2011 8:01 pm
Awesome question! thanks..
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