In a row of girls, Aruna is the first girl from one end. There are 8 girls between Aruna and Bimla. There are 5 girls between Bimla and Chetna. If there are 14 girls standing after Chetna in the row, then what is the minimum possible total number of girls in the row?

Introduction / Context:
This problem is a classic example of position and distance reasoning in a row arrangement. You are given the relative positions of three girls, Aruna, Bimla and Chetna, as well as information about how many girls stand between them and after one of them. The goal is to determine the minimum possible number of girls in the entire row. Such questions are common in verbal and arithmetic reasoning and test your ability to convert verbal descriptions into a positional model.

Given Data / Assumptions:
- Aruna is the first girl in the row, so she stands at position 1 from the left. - There are 8 girls between Aruna and Bimla. - There are 5 girls between Bimla and Chetna. - There are 14 girls standing after Chetna in the same row. - We are asked for the minimum possible total number of girls in the row.

Concept / Approach:
The key idea is to convert between the number of girls between two positions and their numeric positions in the row. If there are k girls between two persons, their positions differ by k + 1. Aruna is fixed at position 1, so Bimla has a fixed position relative to her. Chetna can be placed either to the right or to the left of Bimla with 5 girls between them. Each scenario implies a different total length of the row, once we also account for the 14 girls after Chetna. Among these scenarios, we must select the one that yields the smallest possible total number of girls.

Step-by-Step Solution:
Step 1: Since Aruna is first, assign her position as 1. Step 2: There are 8 girls between Aruna and Bimla, so the distance between Aruna and Bimla is 8 + 1 = 9 positions. Thus, Bimla stands at position 1 + 9 = 10 from the left. Step 3: There are 5 girls between Bimla and Chetna. This means the distance between their positions is 5 + 1 = 6 positions. Step 4: Case 1: Chetna is to the right of Bimla. Then her position is 10 + 6 = 16. If 14 girls stand after Chetna, they occupy positions 17 to 30, giving a total of 30 girls in this configuration. Step 5: Case 2: Chetna is to the left of Bimla. Then her position is 10 - 6 = 4. If 14 girls stand after Chetna, they occupy positions 5 to 18, so the last position in the row is 18, and there are 18 girls in total. Step 6: Both configurations satisfy the given conditions, but the question explicitly asks for the minimum possible number of girls, which is 18 from Case 2.

Verification / Alternative check:
Verify that Case 2 really satisfies all statements. With Aruna at position 1 and Bimla at position 10, there are indeed 8 girls between them at positions 2 through 9. Chetna is at position 4, so between Bimla at 10 and Chetna at 4 there are girls at positions 5, 6, 7, 8 and 9, a total of 5 girls. From Chetna at 4 to the end of the row at position 18, there are girls at positions 5 through 18, giving 14 girls after Chetna. All conditions are met, and the row length is 18.

Why Other Options Are Wrong:
- Totals such as 13, 15 or 16 are too small to accommodate the distances and counts specified, especially the requirement of 14 girls after Chetna. - Any total less than 18 would fail to provide enough positions beyond Chetna to place 14 girls after her. - Although a larger total such as 20 is possible in some alternative arrangements, the question asks for the minimum possible, so such larger numbers are not correct answers.

Common Pitfalls:
Students often forget that when two persons have k people between them, their positions differ by k + 1, not just k. Another frequent error is to assume that the second person must always be to the right, whereas here Chetna can be on either side of Bimla. Ignoring one of the possible directions can lead to missing the minimum configuration. Carefully considering both cases and then comparing their totals avoids these mistakes.

Final Answer:
The minimum possible total number of girls in the row is 18.