A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in :

Part emptied by the leak in 1 hour $=frac{1}{8}-frac{1}{10}=frac{5-4}{40}=frac{1}{40}$ ∴ The leak will empty the cistern in 40 hours. Alternative:

Efficiency fo (A + B) = 4 unit

Efficiency of B = 4 – 5 = – 5

’–’ sign showing B empty.

Time taken to empty the tank by leakage

$=frac{ ext { Capacity of tank }}{ ext { Efficiency of } mathrm{B}}$

$=frac{40}{-1}=40$ hour (Ignore negative sign)