A pipe can fill a tank in 6 hours, and another pipe can fill the same tank in 8 hours. If both pipes are opened at the same time, how long (in hours, rounded off to one decimal place) will it take to fill the tank?

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  1. 4 hours 
  2. hours 
  3. 3.4 hours 
  4. 2.5 hours 

Answer (Detailed Solution Below)

Option 3 : 3.4 hours 
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Detailed Solution

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Given:

Time taken by the first pipe to fill the tank = 6 hours

Time taken by the second pipe to fill the tank = 8 hours

Both pipes are opened simultaneously.

Formula Used:

Efficiency = Total Work / Time taken

Combined efficiency = Efficiency of first pipe + Efficiency of second pipe

Time taken to fill the tank together = Total Work / Combined efficiency

Calculation:

LCM of 6 and 8 = 24. Let the Total Work (capacity of the tank) = 24 units.

Efficiency of the first pipe = 24 / 6 = 4 units/hour.

Efficiency of the second pipe = 24 / 8 = 3 units/hour.

Combined efficiency when both pipes are open = Efficiency of first pipe + Efficiency of second pipe = 4 + 3 = 7 units/hour.

Time taken to fill the tank together = Total Work / Combined efficiency = 24 / 7 hours.

⇒ 24 ÷ 7 ≈ 3.42857... ≈ 3.4 hours.

It will take approximately 3.4 hours to fill the tank if both pipes are opened at the same time.

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