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.

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.