Tap A can fill a pool in 0.4 hours and Tap B can fill the same pool in

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A takes 0.4 hrs = .4 * 60 = 24 mins to do the work alone
B takes 8/15 hrs = 8/15 * 60 = 32 mins to do the work alone

A works for the whole time of 18 mins so it completes 18/24 = 3/4th of the work.

B does the rest 1/4th of the work in whatever time it is on.
Time = Work/Rate = (1/4) / (1/32) = 8 mins

Answer (C)

Tap A can fill a tank in 24 minutes which means that 1/24th of the tank will be filled up in a minute
Tap B can fill a tank in 32 minutes which means that 1/32nd of the tank will be filled up in a minute

and given that A is open for 18 mins --> 18/24 or 3/4th of the tank will be filled and B has to fill the remaining 1/4th of the tank.

B will fill the entire tank in 32 mins and for it to fill 1/4 th of the tank it will take (32/4) = 8 mins.

Since the time taken to fill the pool completely is given in minutes, convert the times taken by the individual taps to minutes.

0.4 hours = \(\frac{2}{5}\) hours = \(\frac{2}{5}\) * 60 = 24 minutes

\(\frac{8}{15}\) hours = \(\frac{8}{15}\) * 60 = 32 minutes

Let the capacity of the pool = LCM (24, 32) = 96 gallons
Therefore,
Rate at which Tap A fills the pool = \(\frac{96 }{ 24}\) = 4 gallons per minute

Rate at which Tap B fills the pool = \(\frac{96 }{ 32}\) = 3 gallons per minute

Let the time after which Tap B has to be turned off = x minutes
This means that both taps worked simultaneously for x minutes
Rate at which Tap A and B fill the pool when working simultaneously = 4 + 3 = 7 gallons per minute.

Since they worked simultaneously for x minutes, work done by them = 7x gallons
After Tap B was shut off, Tap A worked alone for (18 – x) minutes since the total time taken to fill the pool is 18 minutes

Therefore, 7x + 4 (18 – x) = 96
Solving the equation for x, we have x = 8

Tap B should be turned off after 8 minutes

The correct answer option is C.

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