Delhi is bigger than Pune, Kanpur is bigger than Raipur. Jhansi is not

Delhi is bigger than Pune, Kanpur is bigger than Raipur. Jhansi is not as big as Pune, but is bigger than Kanpur. Which one of the following is the smallest city ?

Delhi
Pune
Kanpur
Raipur
This question was previously asked in
UPSC CISF-AC-EXE – 2018
The smallest city is Raipur.
We are given the following comparisons regarding size:
1. Delhi is bigger than Pune: Delhi > Pune
2. Kanpur is bigger than Raipur: Kanpur > Raipur
3. Jhansi is not as big as Pune (i.e., smaller than Pune): Jhansi < Pune 4. Jhansi is bigger than Kanpur: Jhansi > Kanpur

Let’s combine these inequalities:
From (3) and (4): Pune > Jhansi and Jhansi > Kanpur. Combining these gives Pune > Jhansi > Kanpur.
From (2) and the result above (Jhansi > Kanpur): Jhansi > Kanpur > Raipur.
From (1) and the result Pune > Jhansi: Delhi > Pune > Jhansi.

Combining all the relationships, we get a clear order of size:
Delhi > Pune > Jhansi > Kanpur > Raipur.

The city at the smaller end of this chain is Raipur.

The comparisons allow us to establish a strict linear ordering of the four cities by size: Delhi is the largest, followed by Pune, then Jhansi, then Kanpur, and finally Raipur is the smallest.
Delhi > Pune
Pune > Jhansi (from Jhansi < Pune) Jhansi > Kanpur
Kanpur > Raipur
Combining these gives Delhi > Pune > Jhansi > Kanpur > Raipur.
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