Two pipes P and Q can fill a tank in 6 hours and 8 hours respectively. If they are opened on alternate hours and if pipe P is opened first, in how many hours, the tank shall be full ?a)10 hrsb)9.30hrsc)6.45hrsd)10.30hrse)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Let total capacity of tank is 24 units
so P will fill 4 units in 1 hr
Q will fill 3 units in 1 hr.

so in 2 hrs, total (4+3)= 7 units will be filled

in 6 hrs, 21 units will be filled
remaining 3 units, it will be P's turn so P will take
(3/4)*60 = 0.45 hrs

so total time to fill tank is 6.45 hrs

Answer

Problem: Two pipes P and Q can fill a tank in 6 hours and 8 hours respectively. If they are opened on alternate hours and if pipe P is opened first, in how many hours, the tank shall be full ?

Solution:

Let's assume that the total capacity of the tank is 'C'.

Pipe P can fill the tank in 6 hours, which means that in 1 hour, it can fill 1/6th of the tank.

Pipe Q can fill the tank in 8 hours, which means that in 1 hour, it can fill 1/8th of the tank.

Now, let's see how much of the tank will be filled in the first 2 hours (when both pipes are open):

In the first hour:

- Pipe P will fill 1/6th of the tank
- Pipe Q will fill 1/8th of the tank

Together, they will fill:

1/6 + 1/8 = 7/24 of the tank

In the second hour:

- Pipe Q will fill 1/8th of the tank
- Pipe P will fill another 1/6th of the tank

Together, they will fill:

1/8 + 1/6 = 7/48 of the tank

So, in the first 2 hours, they will fill:

7/24 + 7/48 = 14/48 = 7/24 of the tank

After the first 2 hours, pipe P will be closed and pipe Q will fill the tank alone.

In the third hour:

- Pipe Q will fill 1/8th of the tank

So, after 3 hours, the tank will be filled:

7/24 + 1/8 = 11/24 of the tank

After the third hour, pipe Q will be closed and pipe P will fill the tank alone.

In the fourth hour:

- Pipe P will fill 1/6th of the tank

So, after 4 hours, the tank will be filled:

11/24 + 1/6 = 13/24 of the tank

After the fourth hour, pipe Q will be opened again.

In the fifth hour:

- Pipe Q will fill 1/8th of the tank

So, after 5 hours, the tank will be filled:

13/24 + 1/8 = 19/24 of the tank

After the fifth hour, pipe P will be opened again.

In the sixth hour:

- Pipe P will fill 1/6th of the tank

So, after 6 hours, the tank will be filled:

19/24 + 1/6 = 4/6 = 2/3 of the tank

Therefore, the tank will be full in 6.45 hours (approximately).

Hence, the correct option is (c).

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