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by rajan_agarwal » Mon Dec 07, 2015 2:49 am
Q. P Q R can fill the tank in 10, 12, 15 minutes respectively. All the taps were open, and after 90 secs Q n R were closed, find how much time P will take to fill the tank
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by [email protected] » Mon Dec 07, 2015 9:37 am
Hi rajan_agarwal,

If these are GMAT questions, then you should include the 5 answer choices.

To answer this question, we should convert each of the rates into the fraction of the tank that is filled by each per MINUTE.

Tap P fills 1/10 of the tank in 1 minute
Tap Q fills 1/12 of the tank in 1 minute
Tap R fills 1/15 of the tank in 1 minute

As a group, in 1 minute they fill fill 1/10 + 1/12 + 1/15 = 18/180 + 15/180 + 12/180 = 45/180 = 1/4 of the tank..

Since 90 seconds = 1.5 minutes, after 90 seconds (3/2)(1/4) = 3/8 of the tank will be filled. Once Tap Q and Tap R are closed, Tap P will have to fill the remaining portion of the tank (5/8) on its own.

Given that it fills 1/10 per minute...

(5/8) / (1/10) =
50/8 =
6 1/4 minutes

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