Question : On a river, Q is the midpoint between two points, P and R, on the same bank of the river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours and 40 minutes. How long would it take to go from R to P?

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

Option 2: $5$ hours

Option 3: $6\frac{2}{3}$ hours

Option 4: $7\frac{1}{3}$ hours

Question : In covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes longer than B to reach the destination. The time taken by A to reach the destination is:

Option 1: 1 hour

Option 2: 1$\frac{1}{2}$   hours

Option 3: 2 hours

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

Question : A water tap fills a tub in '$p$' hours and a sink at the bottom empties it in '$q$' hours. If $p < q$, both tap and sink are open, and the tank is filled in '$r$' hours, then:

Option 1: $\frac{1}{r}$ = $\frac{1}{p}+\frac{1}{q}$

Option 2: $\frac{1}{r}$ = $\frac{1}{p}-\frac{1}{q}$

Option 3: $r = p + q$

Option 4: $r = p - q$

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 : The value of $\frac{p^{2}- (q - r)^{2}}{(p + r)^{2} - (q)^{2}}$ + $\frac{q^{2} - (p - r)^{2}}{(p + q)^{2} - (r)^{2}}$ + $\frac{r^{2}- (p - q)^{2}}{(q + r)^{2} - (p)^{2}}$ is:

Option 1: 1

Option 2: 2

Option 3: 0

Option 4: 3

Question : If $p+q+r=pqr=\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1$, find $\mathrm{p}^3+\mathrm{q}^3+\mathrm{r}^3$.

Option 1: 1

Option 2: –1

Option 3: 5

Option 4: –5