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Two pipes C and D can fill a tank in 6 hours and 9 hours, respectively. They are opened alternately for 1 hour each, starting with C first. In what du
Question

Two pipes C and D can fill a tank in 6 hours and 9 hours, respectively. They are opened alternately for 1 hour each, starting with C first. In what duration, will the tank be filled?

A.

5 hours

B.

6 hours

C.

8 hours

D.

7 hours

Correct option is D

Given:

- Pipe C can fill the tank in 6 hours.

- Pipe D can fill the tank in 9 hours.

- They are opened alternately for 1 hour each, starting with Pipe C.

Capacity of the tank = LCM of the time taken by A and B. 

Solution:

Capacity of the tank = 18 units

A’s efficiency = 18/6 = 3 units per hour

B’s efficiency = 18/9 = 2 units per hour

2 hours work for A and B = (3 + 2) = 5 units

=> 2 × 3 hours = 3 × 5 or 15 units

=> 6 hours = 15 units

=> 7 hours = 18 units. (At last A fills remaining 3 units)

∴ Tank will be filled in 7 hours.

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