Multiple choice

Passage

Directions: Study the table and answer the question that follows. The given table shows the number of seats reserved in different classes in a train on six days of a week. The number of seats available in each class is given in brackets. Day 2 nd Class Non-AC (900) 1 st Class Non-AC (400) AC III Tier (500) AC II Tier (300) AC 1 st Class (120) Monday 690 240 340 195 70 Tuesday 720 250 410 240 90 Wednesday 840 280 360 175 85 Thursday 800 360 420 160 95 Friday 750 275 350 170 100 Saturday 760 320 380 230 108

If the data related to vacant seats for AC II Tier on the given six days is represented by a pie chart, then what is the difference (in degrees) between the central angles of the sectors representing vacant seats in these classes on Thursday and Monday?

  1. 18°

  2. 25°

  3. 24°

  4. 20°
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The AC II Tier vacant seats are: Monday (300-195=105), Tuesday (300-240=60), Wednesday (300-175=125), Thursday (300-160=140), Friday (300-170=130), Saturday (300-230=70). Total vacant seats = 105+60+125+140+130+70 = 630. Angle per seat = 360/630 = 4/7 degrees. Difference between Thursday (140) and Monday (105) is 35 seats. Difference in angle = 35 * (4/7) = 20 degrees.

AI explanation

First, determine the number of vacant seats for AC II Tier on each day by subtracting the reserved seats from the total available capacity of 300. For Thursday, the vacant seats are 300 minus 160 equals 140; for Monday, they are 300 minus 195 equals 105. Calculate the total vacant seats across all six days: 105 + 60 + 125 + 140 + 130 + 70 equals 630. Find the difference in central angles using the formula (difference in vacant seats divided by total vacant seats) multiplied by 360 degrees, which is ((140 minus 105) divided by 630) times 360, equaling 20 degrees.

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