Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were number-based puzzles. The winner of the competition was the one who solved all puzzles in the least time. The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

How many minutes did Suranjan take to solve the third visual puzzle in the competition?

The correct answer is 2.

Step-by-step Explanation:

1. Determine which puzzles in the sequence are visual puzzles:
The competitors solve 10 puzzles in a fixed sequence from 1 to 10. A competitor starts working on a puzzle as soon as they solve the previous one. By comparing the two charts for a competitor, we can identify the puzzle numbers that are visual puzzles.
Let us analyze Koushik's progress (represented by the green line):

• Koushik solves his 1^st puzzle at 2 minutes (from the "All puzzles" chart), and his visual puzzle count increases to 1 at 2 minutes. This means Puzzle 1 is a visual puzzle (the 1^st visual puzzle).
• Koushik solves his 4^th puzzle at 12 minutes, and his visual puzzle count increases to 2 at 12 minutes. This means Puzzle 4 is a visual puzzle (the 2^nd visual puzzle).
• Koushik solves his 8^th puzzle at 25 minutes, and his visual puzzle count increases to 3 at 25 minutes. This means Puzzle 8 is a visual puzzle (the 3^rd visual puzzle).

Thus, the 3^rd visual puzzle in the competition is Puzzle 8.

2. Calculate the time Suranjan took to solve the 3^rd visual puzzle (Puzzle 8):
Suranjan (represented by the blue line) started working on Puzzle 8 immediately after solving Puzzle 7.
Looking at the "All puzzles" chart for Suranjan (blue line):

• Suranjan solved Puzzle 7 at 28 minutes (the blue line steps up to 7 at $t=28$).
• Suranjan solved Puzzle 8 at 30 minutes (the blue line steps up to 8 at $t=30$).

Therefore, the time Suranjan spent on solving Puzzle 8 is:
$30-28=2\text{ minutes}$