Question : A hemispherical tank full of water is emptied by a pipe at the rate of 7.7 litres per second. How much time (in hours) will it take to empty $\frac{2}{3}$ part of the tank, if the internal radius of the tank is 10.5 m?

Option 1: $\frac{185}{3}$

Option 2: $\frac{185}{6}$

Option 3: $\frac{175}{3}$

Option 4: $\frac{175}{2}$

Question : Pipe A can fill an empty tank in 6 hours and pipe B, in 8 hours. If both pipes are opened and after 2 hours, pipe A is closed, how much time will B take to fill the remaining tank?

Option 1: $7\frac{1}{2}$ hours

Option 2: $2\frac{2}{5}$ hours

Option 3: $2\frac{1}{3}$ hours

Option 4: $3\frac{1}{3}$ hours

Question : An inlet pipe can fill an empty tank in $4 \frac{1}{2}$ hours, while an outlet pipe drains a filled tank in $7 \frac{1}{5}$ hours. The tank is initially empty, and the two pipes are alternately opened for an hour each, till the tank is filled, starting with the inlet pipe. In how many hours will the tank be filled?

Option 1: 24 hours

Option 2: $20 \frac{1}{4}$ hours

Option 3: $20 \frac{3}{4}$ hours

Option 4: $22 \frac{3}{8}$ hours

Question : Pipe A can fill an empty tank in 18 hours and Pipe B can fill the same empty tank in 24 hours. If both the pipes are opened simultaneously, how much time (in hours) will it take to fill the empty tank?

Option 1: $11 \frac{3}{7}$

Option 2: $10 \frac{1}{7}$

Option 3: $10 \frac{2}{7}$

Option 4: $11 \frac{2}{7}$

Question : Two pipes, S1 and S2, can alone fill an empty tank in 15 hours and 20 hours, respectively. Pipe S3 alone can empty that filled tank in 40 hours. Firstly, both pipes, S1 and S2, are opened and after 2 hours, pipe S3 is also opened. In how much time will the tank be filled after S3 is opened?

Option 1: $\frac{90}{17}\ \text{hours}$

Option 2: $\frac{89}{12}\ \text{hours}$

Option 3: $\frac{90}{13}\ \text{hours}$

Option 4: $\frac{92}{11}\ \text{hours}$

Question : A tap can fill a tank in $5 \frac{1}{2}$ hours. Because of a leak, it took $8 \frac{1}{4}$ hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?

Option 1: $\frac{99}{20}$

Option 2: $\frac{5}{2}$

Option 3: $\frac{9}{2}$

Option 4: $\frac{17}{2}$