For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

The correct answer is 23.91%.

This is a Data Interpretation problem typically based on a table or bar chart showing constituency-wise election data — including total valid votes, votes received by each candidate, and the threshold for retaining a security deposit. Let us walk through the full reasoning and methodology step-by-step.

Step 1: Understand the Security Deposit Rule

Under Indian election law, a candidate must secure more than 1/6th (≈ 16.67%) of the total valid votes polled in their constituency to retain their security deposit. Any candidate who fails to achieve this threshold loses their security deposit. So:

$$\text{Security Deposit Threshold}=\frac{1}{6}\times \text{Total Valid Votes in that Constituency}$$

Any candidate whose vote count is less than or equal to this threshold is classified as having lost their security deposit.

Step 2: Identify Candidates Who Lost Their Security Deposit

For each of the four constituencies, you must:

1. Calculate 1/6th of the total valid votes for that constituency.
2. Check each candidate's vote tally against this threshold.
3. List all candidates whose votes fall below the threshold — these are the candidates who lost their deposit.

Step 3: Sum Up the Votes of All Deposit-Losing Candidates (Numerator)

Once identified across all four constituencies, add together the votes received by every such candidate. Let this combined total be denoted as V_lost.

Step 4: Sum Up Total Valid Votes Across All Four Constituencies (Denominator)

Add the total valid votes from each of the four constituencies together. Let this grand total be denoted as V_total.

Step 5: Compute the Required Percentage

Apply the standard percentage formula:

$$\text{Required \%}=\frac{V_{\text{lost}}}{V_{\text{total}}}\times 100$$

Step 6: Arriving at the Answer

When the values from the data table (across all four constituencies) are correctly plugged into the formula above, the result works out to approximately:

$$\frac{V_{\text{lost}}}{V_{\text{total}}}\times 100\approx 23.91\%$$

Why Not the Other Options?

• 23.54% — This is a close distractor, likely arising from a minor arithmetic error such as using a slightly different threshold or accidentally excluding one qualifying candidate from a constituency.

• 32.00% — This value is significantly higher. It would result from incorrectly including candidates who merely came second or third, regardless of whether they crossed the 1/6th threshold, thereby inflating the numerator.

• 38.25% — This is the highest distractor, likely arising from counting all losing candidates (i.e., everyone except the winner) rather than only those who specifically failed to retain their deposit.

Key Takeaway: The critical distinction in this problem is between a "losing candidate" (anyone who didn't win) and a "candidate who lost their security deposit" (one who failed to secure even 1/6th of valid votes). Only the latter group is counted in the numerator. When this rule is applied consistently and precisely to the data from all four constituencies, the answer evaluates to ≈ 23.91%, which corresponds to Option 1.