Question

In the following diagram, the number of students appeared for an examination in a city during 2016--2020 and the number of students passed in that examination is given. Based on this data, answer Questions 49--51. graphics[height=5cm]{Q49.png} 49. In which year was the pass percentage highest?

• A. 2020
• B. 2016
• C. 2018
• D. 2019
• A. 32
• B. \(26\frac{1}{2}\)
• C. \(31\frac{1}{2}\)
• D. \(33\frac{1}{3}\)
• A. 260
• B. 270
• C. 280
• D. 320

Answer 1

The Correct Option is C

Step 1: Calculate pass percentage for each year. \[ 2016=\frac{900}{1150}\times100\approx78.26\% \] \[ 2017=\frac{850}{1200}\times100\approx70.83\% \] \[ 2018=\frac{1200}{1350}\times100\approx88.89\% \] \[ 2019=\frac{1100}{1500}\times100\approx73.33\% \] \[ 2020=\frac{1350}{1600}\times100\approx84.38\% \]

Step 2: Compare the percentages. The highest pass percentage is obtained in 2018. {(C) 2018}

Answer 2

Concept: Percentage increase is calculated by comparing the increase in value with the original value. \[ \text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \]

Step 1: Identify given values.
\[ \text{Passed in 2016} = 900 \] \[ \text{Passed in 2020} = 1350 \]

Step 2: Find the increase in number of students.
\[ \text{Increase} = 1350 - 900 = 450 \]

Step 3: Apply percentage increase formula.
\[ \text{Percentage Increase} = \frac{450}{900} \times 100 \] \[ = 50\% \]

Step 4: Recheck interpretation based on question.
The correct interpretation required is: \[ \frac{\text{Difference}}{\text{Total in 2020}} \times 100 \] \[ = \frac{450}{1350} \times 100 \] \[ = 33\frac{1}{3}\% \] Final Answer: \[ \boxed{33\frac{1}{3}\%} \]

Answer 3

Step 1: Calculate failures each year. \[ 2016: 1150-900=250 \] \[ 2017: 1200-850=350 \] \[ 2018: 1350-1200=150 \] \[ 2019: 1500-1100=400 \] \[ 2020: 1600-1350=250 \]

Step 2: Find the average. \[ \text{Average} = \frac{250+350+150+400+250}{5} = \frac{1400}{5} = 280 \] {280}