The following chart is showing the number of cars passing in specific place in a morning 6 am to 12 Noon.
Which of the following are true on the basis of data given in chart? A. Highest number of cars are passing between 8 am - 9 am. B. On an average, 90 cars are passing per hours. C. 50\% cars are passing higher in the interval 7 am to 8 am than 6 am to 7 am. D. Less than half cars are passing 11 am - 12 noon than 8 am - 9 am. E. Number of cars passing higher before 9 am than after 8 am. Choose the correct answer from the options given below:
Show Hint
Checking Statement C is extremely fast: \(105 - 70 = 35\), which is exactly half of 70, meaning a 50% increase. Knowing C is true immediately eliminates option (A) and narrows the choices down.
• Step 1: Understanding the Question: This question uses a bar chart of hourly car frequencies from 6:00 AM to 12:00 Noon. We need to extract the data values for each interval and analyze the accuracy of the five comparative statements.
• Step 2: Key Formula or Approach:
1. Read the bar values for each hour:
- 6-7 AM: 70 cars
- 7-8 AM: 105 cars
- 8-9 AM: 130 cars
- 9-10 AM: 115 cars
- 10-11 AM: 95 cars
- 11-12 Noon: 45 cars
2. Perform calculations for average, percentages, and inequalities.
• Step 3: Detailed Explanation:
Let us evaluate each statement:
- Statement A: "Highest number of cars are passing between 8 am - 9 am."
Comparing all values, 130 is the peak. This is between 8 am and 9 am. (True)
- Statement B: "On an average, 90 cars are passing per hours."
Let us sum the cars over all 6 hours:
\[ \text{Total} = 70 + 105 + 130 + 115 + 95 + 45 = 560 \]
\[ \text{Average} = \frac{560}{6} \approx 93.33 \text{ cars per hour} \]
The average is 93.33, not 90. (False)
- Statement C: "50% cars are passing higher in the interval 7 am to 8 am than 6 am to 7 am."
6-7 AM = 70 cars. 7-8 AM = 105 cars.
Increase = \(105 - 70 = 35\).
Percentage Increase:
\[ \frac{35}{70} \times 100 = 50\% \]
This is correct. (True)
- Statement D: "Less than half cars are passing 11 am - 12 noon than 8 am - 9 am."
8-9 AM = 130 cars. Half of this count is 65.
11-12 Noon = 45 cars.
Since \(45 < 65\), it is indeed less than half. (True)
- Statement E: "Number of cars passing higher before 9 am than after 8 am."
Before 9 AM (6-9 AM) = \(70 + 105 + 130 = 305\).
After 8 AM (8-12 Noon) = \(130 + 115 + 95 + 45 = 385\).
Since \(305 < 385\), the count is not higher before 9 AM. (False)
Thus, statements A, C, and D are correct.
• Step 4: Final Answer: Statements A, C, and D are correct, matching option (C).
