Instructions [34 - 37 ]

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.

Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?

Correct Answer: 4.0 minutes

To determine the average time taken by Anirbid to solve the number-based puzzles, we analyze and correlate the two step-charts provided in the image:

1. All Puzzles Chart (Left): This chart shows the cumulative number of puzzles (from 1 to 10) solved by each competitor over time (measured in minutes along the x-axis).
2. Visual Puzzles Chart (Right): This chart displays the cumulative number of visual puzzles (from 1 to 5) solved by each competitor over time.
By tracking Anirbid's progress (indicated by the red line in both charts) and looking at the transition points where each puzzle is completed, we can determine the exact time at which he solved each of the 10 sequential puzzles and identify whether each puzzle was visual or number-based.

Step 1: Identifying the Completion Times for All Puzzles (Left Chart - Red Line)
Looking at the step-up points for the red line in the "All puzzles" chart, we find the completion times for all 10 puzzles:

• Puzzle 1: Completed at 4 minutes
• Puzzle 2: Completed at 9 minutes
• Puzzle 3: Completed at 11 minutes
• Puzzle 4: Completed at 14 minutes
• Puzzle 5: Completed at 19 minutes
• Puzzle 6: Completed at 22 minutes
• Puzzle 7: Completed at 27 minutes
• Puzzle 8: Completed at 29 minutes
• Puzzle 9: Completed at 32 minutes
• Puzzle 10: Completed at 36 minutes

Step 2: Identifying the Completion Times for Visual Puzzles (Right Chart - Red Line)
From the "Visual puzzles" chart, Anirbid (red line) completes visual puzzles at the following times:

• Visual Puzzle 1: Completed at 4 minutes
• Visual Puzzle 2: Completed at 14 minutes
• Visual Puzzle 3: Completed at 29 minutes
• Visual Puzzle 4: Completed at 32 minutes

Since the competition is sequential, we match these visual puzzle completion times with the overall puzzle numbers:

• Puzzle 1 (completed at 4 min) corresponds to Visual Puzzle 1.
• Puzzle 4 (completed at 14 min) corresponds to Visual Puzzle 2.
• Puzzle 8 (completed at 29 min) corresponds to Visual Puzzle 3.
• Puzzle 9 (completed at 32 min) corresponds to Visual Puzzle 4.

Thus, the remaining puzzles (2, 3, 5, 6, 7, and 10) are the 6 number-based puzzles.

Step 3: Calculating Time Taken for Each Number-Based Puzzle
The time taken for any puzzle is the difference between its completion time and the completion time of the previous puzzle:

• Puzzle 2 (Number-based): 9 min - 4 min = 5 minutes
• Puzzle 3 (Number-based): 11 min - 9 min = 2 minutes
• Puzzle 5 (Number-based): 19 min - 14 min = 5 minutes
• Puzzle 6 (Number-based): 22 min - 19 min = 3 minutes
• Puzzle 7 (Number-based): 27 min - 22 min = 5 minutes
• Puzzle 10 (Number-based): 36 min - 32 min = 4 minutes

Step 4: Finding the Average Time
The total time spent by Anirbid on these 6 number-based puzzles is:
$${\text{Total Time}}_{\text{number-based}}=5+2+5+3+5+4=24\text{minutes}$$
Since there are 6 number-based puzzles, the average time taken per puzzle is:
$$\text{Average Time}=\frac{24\text{minutes}}{6}=4.0\text{minutes}$$
Thus, the closest average time taken by Anirbid to solve the number-based puzzles is 4.0 minutes.