The following table shows the percentage (%) of girls who passed in an examination and the percentage (%) of boys who failed in that exam in a school during the six years from 2018 to 2023. Based on the data in the table, answer the questions that follow.
Year-wise Result details of Students
Year Percentage of Girls who passed Percentage of Boys who failed 2018 32% 40% 2019 42% 60% 2020 55% 25% 2021 40% 30% 2022 60% 50% 2023 42% 80%
Understanding Exam Results Ratio Calculation
This problem requires calculating the ratio between the number of boys who passed and the number of girls who failed in a specific year (2020), using the provided examination data.
Exam Data Table for Reference
The table below shows the percentage (%) of girls passing and the percentage (%) of boys failing over six years.
| Year | Percentage of Girls who passed | Percentage of Boys who failed |
|---|---|---|
| 2018 | 32% | 40% |
| 2019 | 42% | 60% |
| 2020 | 55% | 25% |
| 2021 | 40% | 30% |
| 2022 | 60% | 50% |
| 2023 | 42% | 80% |
Calculating the Number of Boys Passed in 2020
We are given the following information for the year 2020:
- Total number of boys appeared = 800
- Percentage of boys who failed = 25%
To find the number of boys who passed, we first need to find the percentage of boys who passed:
Percentage of boys passed = $100\% - \text{Percentage of boys who failed}$
Percentage of boys passed = $100\% - 25\% = 75\%$
Now, we calculate the total number of boys who passed:
Number of boys passed = $75\%$ of $800$
Number of boys passed = $\frac{75}{100} \times 800$
Number of boys passed = $0.75 \times 800 = 600$
Calculating the Number of Girls Failed in 2020
We are given the following information for the year 2020:
- Total number of girls appeared = 700
- Percentage of girls who passed = 55%
To find the number of girls who failed, we first calculate the percentage of girls who failed:
Percentage of girls failed = $100\% - \text{Percentage of girls who passed}$
Percentage of girls failed = $100\% - 55\% = 45\%$
Now, we calculate the total number of girls who failed:
Number of girls failed = $45\%$ of $700$
Number of girls failed = $\frac{45}{100} \times 700$
Number of girls failed = $0.45 \times 700 = 315$
Determining the Ratio
The question asks for the ratio of the total number of boys who passed to the total number of girls who failed in 2020.
Ratio = (Number of boys passed) : (Number of girls failed)
Ratio = $600 : 315$
To simplify the ratio, we find the greatest common divisor (GCD) of 600 and 315.
- Prime factorization of 600: $2^3 \times 3 \times 5^2$
- Prime factorization of 315: $3^2 \times 5 \times 7$
- GCD(600, 315) = $3 \times 5 = 15$
Now, we divide both parts of the ratio by the GCD (15):
Simplified Ratio = $\frac{600}{15} : \frac{315}{15}$
Simplified Ratio = $40 : 21$
Final Answer Explanation
The calculated ratio of the total number of boys who passed to the total number of girls who failed in 2020 is 40:21.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 Who had the best score on either test?
Who had the most consistent scores on both tests?
Who had the least consistent scores on both tests?
Who had the poorest score on either test?
