Question

Four pipes A, B, C and D can fill a tank with water in 15, 20, 30 and 60 hours respectively.

Pipe A is opened at 4 a.m., B at 5 a.m., C at 6 a.m. and D at 7 a.m. When is the tank filled up completely?
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Answer 1

Answer:

1:30 pm

Step-by-step explanation:

Answer 2

At 11 am the tank is filled.

Given:

Four pipes A, B, C, and, D can fill a tank in 15, 20, 30, and 60 hours respectively with water.

To Find:

When will the tank fill up completely?

Solution:

Pipe A can fill a tank with water in 15 hours.

⇒  In 1 hour, Pipe A can fill 1/15 of the tank.

Similarly,

In 1 hour, Pipe B can fill 1/20 of the tank.

In 1 hour, Pipe C can fill 1/30 of the tank.

In 1 hour, Pipe D can fill 1/60 of the tank.

At 4 am Pipe A is opened. Let pipe A takes t hours to fill the tank.

After one hour Pipe B is opened. Therefore it takes (t-1) hours

.After two hours Pipe C is opened. Consequently, it takes (t-2) hours.

After three hours Pipe D is opened . Consequently, it takes (t-3) hours.

Now, To fill the tank

t/ 15 + (t-`1)/20 + (t-2)/30 + (t-3)/60 = 1

( 4t + 3t -3 + 2t -4 +t -3)/60 = 1

(10t - 10 ) /60 = 1

⇒ 10t -10 = 60

⇒ 10t = 10+60

⇒ t = 70/10

⇒ t = 7

∴ It takes 7 hours to fill the tank.

Pipe A is opened at 4 am

⇒ ( 4 am +7 hours) = 11 am

∴ At 11 am the tank is filled completely.

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