Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:

$$ \begin{aligned} & P < Q \\ & S > P > T \\ & R < T \end{aligned} $$

If integers 1 through 5 are used to construct such a number, the value of $P$ is:

A business person buys potatoes of two different varieties $P$ and $Q$, mixes them in a certain ratio and sells them at ₹192 per kg.

The cost of the variety P is $Rs\,800$ for 5 kg .

The cost of the variety Q is $Rs\, 800$ for 4 kg .

If the person gets $8 \%$ profit, what is the $\mathrm{P}: Q$ ratio (by weight)?

Three villages $P, Q$, and $R$ are located in such a way that the distance $P Q=13 \mathrm{~km}$, $Q R=14 \mathrm{~km}$, and $R P=15 \mathrm{~km}$, as shown in the figure. A straight road joins $Q$ and $R$. It is proposed to connect $P$ to this road $Q R$ by constructing another road. What is the minimum possible length (in km ) of this connecting road?

Note: The figure shown is representative.