# Two pipes, A and B, can fill a tank in 6 hours and 8 hours respectively. If they are opened alternately for one hour, and A is opened first, how much

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Two pipes, A and B, can fill a tank in 6 hours and 8 hours respectively. If they are opened alternately for one hour, and A is opened first, how much time will it take to fill the tank?
1. 5 hours 50 minutes
2. 6 hours 50 minutes
3. 5 hours 45 minutes
4. 6 hours 45 minutes

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Correct Answer - Option 4 : 6 hours 45 minutes

Calculation:

According to the question:

A's work in 1 hour = 1/6

B's work in 1 hour = 1/8

(A + B)'s 2 hours work when opened alternately = 1/6 + 1/8

⇒ (4 + 3)/24 = 7/24

(A + B)'s 6 hours work when opened alternately = (7/24) × 3 = 21/24

⇒ 7/8

Now,

Remaining part = 1 – 7/8 = 1/8

It is A's turn and 1/6 part is filled by 1 hour.

1/8 part filled by A = 6 × 1/8 = 3/4 hour

⇒ (3/4 × 60) = 45 minutes

Total time = (6 + 45 minutes) = 6 hours 45 minutes.

∴ Time taken to fiil the tank is 6 hours 45 minutes.