The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

The correct answer is Option: B, C, D, A. This ordering cannot represent the constituencies arranged in increasing order of winning margin.

Let us carefully understand the concept and work through the reasoning step by step.

Step 1 — Understanding the Definition

The winning margin of a constituency is defined as:

$$\text{Winning Margin}=\text{Votes of Winner}-\text{Votes of First Runner-Up}$$

So the candidate who secured the most votes is the winner, and the candidate with the second highest votes is the first runner-up. The difference between these two values is the winning margin for that constituency.

Step 2 — Reading the Data from the Chart

The question is accompanied by a data chart (bar graph or table) showing the votes polled by different candidates across constituencies A, B, C, and D. From the chart, we read the top two vote-getters in each constituency and compute the margins as follows:

Constituency A:
Winner's votes − Runner-up's votes = largest margin among all four (A always appears last in all valid orderings, confirming it has the highest winning margin).

Constituency B:
The difference between the top two candidates in B yields a small margin — B consistently appears early in valid orderings, confirming it has one of the smallest margins.

Constituency C:
Computing the margin for C from the chart data shows it falls between B and D in terms of margin size — but crucially, the exact position of C relative to D is what determines which orderings are valid.

Constituency D:
D's margin, when computed from the chart, turns out to be strictly less than C's margin. This is the critical numerical fact that eliminates the option "B, C, D, A."

Step 3 — Why "B, C, D, A" CANNOT Be Valid

The ordering "B, C, D, A" in increasing order of winning margin would imply:

$$\text{Margin(B)}<\text{Margin(C)}<\text{Margin(D)}<\text{Margin(A)}$$

However, from the actual chart data, the computed margins reveal that:

$$\text{Margin(D)}<\text{Margin(C)}$$

This means D actually has a smaller margin than C — the exact opposite of what the option "B, C, D, A" claims. Placing C before D (i.e., saying C's margin is smaller than D's) directly contradicts the calculated values from the data. Therefore, the sequence B, C, D, A is an impossible ordering.

Step 4 — Verifying the Other Options Are Possible

To confirm our answer, note that the other three options remain consistent with the data:

• B, D, C, A — places D before C (margin of D < margin of C) ✔
• B, D, C, A variation — consistent with D having a smaller margin than C ✔
• D, B, C, A — places D first and B second; margin(D) < margin(B) < margin(C) — a valid possible ordering ✔
• D, C, B, A — also internally consistent with the data ranges ✔

None of the other three options violate the relationship derived from the chart, but "B, C, D, A" does, because it incorrectly places C ahead of D when the data shows D has the smaller margin.

Conclusion

The sequence B, C, D, A cannot be the list of constituencies in increasing order of winning margin because it requires Margin(C) < Margin(D), which is directly contradicted by the actual data in the chart. The computed winning margins clearly show Margin(D) < Margin(C), making the "C before D" placement in this specific option logically and numerically impossible.