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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?
Comparing the 1st and 2nd graphs, we should be able to determine the type of puzzle.
From the second graph, we can say that there are 4 visual-based puzzles in total, which makes the number-based puzzles 6.
Let us follow the green line in both graphs:
The 1st visual-based puzzle was completed by Green in 2 minutes from the 2nd graph. From the 1st graph at the 2nd minute, the puzzle that was solved by Green was 1. So, we can say that 1 is a visual-based puzzle.
The 2nd visual-based puzzle was completed by Green in 12 minutes from the 2nd graph. From the 1st graph at the 12th minute, the puzzle that was solved by Green was 4. So, we can say that 4 is a visual-based puzzle.
The 3rd visual-based puzzle was completed by Green in 25 minutes from the 2nd graph. From the 1st graph at the 25th minute, the puzzle that was solved by Green was 8. So, we can say that 8 is a visual-based puzzle.
The 4th visual-based puzzle was completed by Green in 29 minutes from the 2nd graph. From the 1st graph at the 29th minute, the puzzle that was solved by Green was 9. So, we can say that 9 is a visual-based puzzle.
We can conclude that puzzles 1, 4, 8, and 9 are visual-based, while puzzles 2, 3, 5, 6, 7, and 10 are number-based.
The average time taken by Anirbid to solve the number-based puzzles can be calculated as,
Time for 1st number-based puzzle(2nd puzzle) from 1st graph = 9 - 4 = 5 minutes.
Time for 2nd number-based puzzle(3rd puzzle) from 1st graph = 11 - 9 = 2 minutes.
Time for 3rd number-based puzzle(5th puzzle) from 1st graph = 19 - 14 = 5 minutes.
Time for 4th number-based puzzle(6th puzzle) from 1st graph = 22 - 19 = 3 minutes.
Time for 5th number-based puzzle(7th puzzle) from 1st graph = 27 - 22 = 5 minutes.
Time for 6th number-based puzzle(10th puzzle) from 1st graph = 37 - 33 = 4 minutes.
Average $$=\ \dfrac{5\ +\ 2\ +\ 5\ +\ 3\ +\ 5\ +\ 4}{6}\ =\ \dfrac{24}{6}\ =\ 4$$ minutes
The average time taken by Anirbid to solve the number-based puzzles is 4 minutes.
Hence, the correct answer is option D.
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