Moderate Pie Charts Solved QuestionData Interpretation Discussion

Common Information

At a famous Wax museum, visitors are allowed to enter or exit the museum only once every hour. On any day the visitors can enter only at any of the five scheduled "let-in" timings — 11:00 a.m., 12:00 noon, 1:00 p.m., 2:00 p.m. and 3:00 p.m. and they can exit only at any of the five schedule "let-out" timings - 12:00 noon, 1:00 p.m., 2:00 p.m., 3:00 p.m. and 4:00 p.m.

The following pie charts give the distribution of all the 1200 visitors to the museum, on 15 August 2007. Pie chart - 1 shows the percentage distribution of the total number of visitors as per the time at which they entered the museum. Pie chart - 2 shows the percentage distribution of the total number of visitors as per the times at which they exited the museum. Each visitor stays in the museum for at least one hour and none of the visitors visit the museum more than once in the day.

 Q. Common Information Question: 4/4 If the number of people who stayed in the museum for exactly two hours is $x$, the minimum and maximum possible values of $x$ are:
 ✖ A. 150 and 660 ✖ B. 0 and 600 ✖ C. 150 and 720 ✔ D. 0 and 720

Solution:
Option(D) is correct

Of those who entered at 11:00 a.m., 150 would have exited at 12:00 p.m. out of 240 who entered at 12:00 p.m.. 180 would have exited at 1:00 p.m. Out of 360 who entered at 1:00 p.m., 180 would have exited at 2:00 p.m. Out of 270 who entered at 2:00 p.m., 270 would have exited at 3:00 p.m. and the 120 persons who entered at 3:00 p.m. with the persons remaining till now would have exited at 4:00 p.m.

Hence, the minimum possible number is 0.

Of the 210 persons who entered at 11:00 a.m., 150 would have exited at 12:00 p.m. and the remaining at 1:00 p.m. Now out of 240 who entered at 12:00 p.m., 120 would have exited at 1:00 p.m. and the remaining 120 at 2:00 p.m. out of 360 who entered at 1:00 p.m., 60 would have exited at 2:00 p.m., 270 would have exited at 3:00 p.m. and 30 at 4:00 p.m. The 270 who entered at 2:00 p.m. would have exited at 4:00 p.m.

Total maximum possible:

$= 60 + 120 + 270 + 270$

$= \textbf{720}$