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 : There are 3 taps A, B, and C in a tank. These can fill the tank in 10 hours, 20 hours, and 25 hours, respectively. At first, all three taps are opened simultaneously. After 2 hours, tap C is closed and A and B keep running. After 4 hours from the beginning, tap B is also closed. The remaining tank is filled by tap A alone. Find the percentage of work done by tap A itself.

Option 1: 32%

Option 2: 75%

Option 3: 52%

Option 4: 72%