An inlet pipe can fill a tank in 4 hours and an outlet pipe can empty

1.	An inlet pipe can fill a tank in 4 hours and an outlet pipe can empty a tank in 3/7 of a tank in 3h. Find the time taken to fill the tank if they start working alternately.1. 125/8 hours2. 127/7 hours3. 121/9 hours4. 129/8 hours5. None of these
Answer» Correct Answer - Option 2 : 127/7 hours Given: Time taken by inlet pipe to fill the tank = 4 hours Time taken by outlet pipe to empty 3/7 of a tank = 3 hours Formula used: Efficiency = Total work/Time taken Calculation: LCM of 4 and 7 = 28 = Total work Efficiency of inlet pipe = 28/4 = 7 work Efficiency of outlet pipe = 28/7 = 4 work Work done in 2 hours = (7 – 4) = 3 work Time taken to do 27 work = (2/3) × 27 hours ⇒ 18 hours Time taken more to complete remaining 1 work = 1/7 hour Total time taken = 18 + (1/7) hours ⇒ 127/7 hours ∴ The total time taken to fill the tank is 127/7 hours

An inlet pipe can fill a tank in 4 hours and an outlet pipe can empty a tank in 3/7 of a tank in 3h. Find the time taken to fill the tank if they start working alternately.1. 125/8 hours2. 127/7 hours3. 121/9 hours4. 129/8 hours5. None of these

Answer» Correct Answer - Option 2 : 127/7 hours

Given:

Time taken by inlet pipe to fill the tank = 4 hours

Time taken by outlet pipe to empty 3/7 of a tank = 3 hours

Formula used:

Efficiency = Total work/Time taken

Calculation:

LCM of 4 and 7 = 28 = Total work

Efficiency of inlet pipe = 28/4 = 7 work

Efficiency of outlet pipe = 28/7 = 4 work

Work done in 2 hours = (7 – 4) = 3 work

Time taken to do 27 work = (2/3) × 27 hours

⇒ 18 hours

Time taken more to complete remaining 1 work = 1/7 hour

Total time taken = 18 + (1/7) hours

⇒ 127/7 hours

∴ The total time taken to fill the tank is 127/7 hours

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