If pipes A and B can fill the tank separately in 3 hours and 4 hours respectively while pipe C can now empty the completely filled tank in 1 hour due to more leakages. If the pipes A, B and C are opened in order at 9, 10 and 11 AM respectively, at what time will the tank be empty ?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1 : 12 PM
Rate of A = $\frac{1}{5}$ tank per hour
Rate of B = $\frac{1}{4}$ tank per hour
Rate of A = $\frac{1}{1}=1$ tank per hour
from 9 AM to 10:00 AM
Water filled = $\frac{1}{3}$ of the tank
from 10:00 AM to 11:00 AM
Water filled = $\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$ of the tank
from 11:00 AM onward,
$\frac{1}{3}+\frac{1}{4}-1=-\frac{5}{12}$
Time required to empty the tank = $\frac{11}{12}×\frac{12}{5}=2.2\,hours$
The tank will be empty by 1:12 PM.