Question : If $P =\frac{96}{95\times97}, Q = \frac{97}{96\times98}$ and $R = \frac{1}{97}$, then which of the following is true?

Option 1: $P < Q < R $

Option 2: $R < Q < P $

Option 3: $Q < P < R $

Option 4: $R < P < Q $

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

Question : The value of $ \frac{(p-q)^3+(q-r)^3+(r-p)^3}{12(p-q)(q-r)(r-p)}$, where $p \neq q \neq r$, is equal to:

Option 1: $\frac{1}{9}$

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

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

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

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