Which is the shortest route from $P$ to $U$, and how long is it?

$P$–$Q$–$S$–$U$, $105$ km

$P$–$R$–$S$–$U$, $105$ km

$P$–$Q$–$T$–$U$, $120$ km

Fuel costs ₹$5$ per km. Taking toll and fuel together, which route from $P$ to $U$ is cheapest, and what does it cost?

$P$–$Q$–$S$–$U$, ₹$705$

$P$–$R$–$S$–$U$, ₹$725$

$P$–$R$–$T$–$U$, ₹$660$

$P$–$Q$–$T$–$U$, ₹$790$

PRACTICE

100:00+4 −1MCQ Single Answer

Data / Set

Six towns — Pali, Quila, Ratan, Sagar, Tilak and Umrah, written below as

P

Q

R

S

T

and

U

— are joined by nine roads. Every road is two-way, and each carries a toll that is paid once, in either direction.

There is no road other than these nine. A driver has to travel from

P

U

. Throughout, a route means a journey that never enters the same town twice.

How many different routes are there from

P

U