Question

1) A cistern can be filled by a pipe in 5 hours and emptied by another pipe in 8 hours.
i) If both pipes are opened together, in what time will the empty cistern be full ?
ii) If the cistern can hold 200 litres, how long would it be before exactly 30 litres had run in ?​

Answer 1

(i) Ok, in each hour (1/5)th of the tank is filled and (1/8)th is emptied
This takes place for x hours (assume)
So in each hour 1/x of the tank is filled
So (1/5 - 1/8) = (1/x) => x = (40/3) hrs

ii) 200 litres are filled in (40/3) hrs
Then 15 litres are filled in 1 hr
Then 30 litres are filled in 2 hrs