Lakshmi, her brother, her daughter and her son are badminton players. A game of doubles is about to begin and they play in the following directions.

Correct Option

The problem involves four players: Lakshmi (L), her brother (LB), her daughter (LD), and her son (LS) in a doubles badminton game. The objective is to identify the best player based on three positional conditions.

• Condition (1) states that Lakshmi's brother (LB) is directly across the net from her daughter (LD). This establishes them as opponents.
• Condition (3) states that the best player and the worst player are on the same side of the net, meaning they are partners.
• Let us assume Lakshmi's brother (LB) is the best player. According to condition (3), the worst player must be on the same side of the net as LB. Given the family structure, Lakshmi is a plausible candidate for the worst player to satisfy condition (3) by partnering with her brother.
• If LB (best player) and L (worst player) are partners on one side of the net, then LD (Lakshmi's daughter) and LS (Lakshmi's son) must be partners on the opposite side.
• Now, let's verify condition (2): "Her son (LS) is diagonally across the net from the worst player’s sibling."
  • If Lakshmi (L) is the worst player, her sibling is Lakshmi's brother (LB).
  • LS is on the opposite side of the net from LB. If LB is at one court position, and L is adjacent to him, then LD is directly opposite LB, and LS is directly opposite L. In this configuration, LS is indeed diagonally across from LB.
• This arrangement satisfies all three conditions, confirming that Lakshmi's brother is the best player and Lakshmi is the worst player.

Incorrect Options

• Options (2) Her daughter, (3) Her son, and (4) Lakshmi are incorrect because they do not allow for a consistent arrangement that satisfies all three given conditions simultaneously. If any of these individuals were considered the best player, the subsequent deductions based on the conditions, particularly the pairing of the best and worst players (condition 3) and the relative positions of the son and the worst player's sibling (condition 2), would lead to contradictions. The unique configuration derived from the conditions identifies Lakshmi's brother as the best player.