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
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