Three girls Banu, Dhivya and Nithya are standing in a queue. There are five…

Concept

In a queue / row puzzle, fix every person to an absolute position number counted from the front. Two relationships are used: "k persons ahead of / behind X" pins X's position directly, while "m persons between X and Y" means the positions of X and Y differ by (m + 1), without by itself telling you which one is in front.

Application

1. "Three girls ahead of Nithya" fixes Nithya at position 4 from the front (3 girls occupy positions 1-3).

2. "Eight girls between Dhivya and Nithya" means their positions differ by 8 + 1 = 9. Since Nithya is at 4, Dhivya is at 4 + 9 = 13 (the value 4 - 9 is negative, so it is rejected).

3. "Five girls between Banu and Dhivya" means their positions differ by 5 + 1 = 6. With Dhivya at 13, Banu is at 13 - 6 = 7 or 13 + 6 = 19.

4. "Twenty-one girls behind Banu" means the total length = Banu's position + 21. For Banu at 7 this gives 7 + 21 = 28; for Banu at 19 it gives 19 + 21 = 40.

5. The puzzle asks for the minimum possible length, so choose the smaller: 28.

Cross-check

Take the queue of length 28 with Nithya = 4, Dhivya = 13, Banu = 7. Girls ahead of Nithya = 3. Girls between Dhivya and Nithya = 13 - 4 - 1 = 8. Girls between Banu and Dhivya = 13 - 7 - 1 = 5. Girls behind Banu = 28 - 7 = 21. Every clue holds, so the minimum number of girls in the queue is 28.