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Two pipes A and B can fill a tank in 24 minutes, and 32 minutes. If both the pipes are opened simultaneously,  after _______ minutes time B should be closed so that the tank is full in 18 minutes .

pls explain.
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(Let B be closed after x minutes. Then,
Part filled by (A+B) in x min+ part filled by A in (18-x)min=1
x(1/24+1/32)+(18-x)*1/24=1
7x/96+18-x/24=1
7x+4(18-x)=96
x=8. Hence, B must be closed after 8 mins. )
@ukn

please see the best chosen answer, hope you will understand it .

8


Let B be closed after x minutes.

Then, Part filled by (A+B) in x min+ part filled by A in (18-x)min = 1

x(1/24+1/32)+(18-x)*1/24=1

7x/96+18-x/24=1 7x+4(18-x)=96

x=8.

Hence, B must be closed after 8 mins.

after _______ minutes time B should be closed so that the tank is full in 18 minutes

Interpretation 1: After x minutes should B be closed, so that A takes 18 minutes to fill the rest of the tank.

ie, it takes 18 minutes AFTER closing B

Interpretation 2: After x minutes should B be closed, so that A fills the rest of the tank, and the total time taken is 18 minutes.

ie, it takes 18 minutes in TOTAL.

Interpretation 1 gives you the answer 3.43 minutes.

Interpretation 2 gives you the answer 8 minutes.

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