A tap can fill a tank in 6 hours after 4 hours it was found that only 60% of the tank is full due to a leakage at the bottom which was then immediately repaired.In how much time will the tank to completely filled?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 6 hours 24 minutes.
Filling rate = 1/6 of the tank per hour
In 4 hours, 4 × 1/6 = 2/3 = 66.67%
But due to leakage, only 60% of the tank was filled
So, actual filled = 3/5
Loss due to leakage in 4 hours = 2/3 − 3/5 = (10 − 9)/15 = 1/15 tank lost in 4 hours
Leakage rate = 1/15 ÷ 4 = 60
So, the effective rate during the first 4 hours = 1/6 − 1/60 = (10 − 1)/60 = 9/60 = 3/20
Now remaining tank to fill = 1 − 3/5 = 2/5
Since the leak is repaired, now the full rate = 1/6
Time to fill 25 of the tank = 25 ÷ 1/6 = 2/5 × 6 = 12/5 = 2.4 hours = 2 hrs 24 min
Total time = 4 hours + 2 hours 24 min = 6 hours 24 min