This question asks us to find the ratio between the number of males who passed from college B and the number of females who failed from college C, given the ratio of the total number of students in college B and college C.

We are given the following information from the table:

• College B: Pass percentage = 55%, Ratio of Male to Female in pass students = 5 ∶ 3, Ratio of Male to Female in fail students = 11 ∶ 14
• College C: Pass percentage = 70%, Ratio of Male to Female in pass students = 7 ∶ 5, Ratio of Male to Female in fail students = 5 ∶ 3

We are also given that the ratio of the total number of students in college B and college C is 2 ∶ 3.

Let the total number of students in college B be $2k$ and the total number of students in college C be $3k$, where $k$ is a proportionality constant.

Calculating Number of Passed and Failed Students

First, we calculate the number of passed and failed students in colleges B and C based on the pass percentages.

• College B:
  • Total students = $2k$
  • Number of passed students in B = 55% of $2k = \frac{55}{100} \times 2k = 0.55 \times 2k = 1.1k$
  • Number of failed students in B = (100% - 55%) of $2k = 45% of $2k = \frac{45}{100} \times 2k = 0.45 \times 2k = 0.9k$
• College C:
  • Total students = $3k$
  • Number of passed students in C = 70% of $3k = \frac{70}{100} \times 3k = 0.70 \times 3k = 2.1k$
  • Number of failed students in C = (100% - 70%) of $3k = 30% of $3k = \frac{30}{100} \times 3k = 0.30 \times 3k = 0.9k$

Calculating Male Pass from B

The ratio of male to female students among passed students in college B is given as 5 ∶ 3. The total parts in this ratio are $5 + 3 = 8$.

The number of male students who passed from college B is a fraction of the total passed students in B, determined by this ratio.

Number of male pass students from B = $\frac{\text{Ratio part for Male}}{\text{Total ratio parts}} \times \text{Total passed students in B}$

Number of male pass students from B = $\frac{5}{8} \times 1.1k = \frac{5.5k}{8}$

Calculating Female Fail from C

The ratio of male to female students among failed students in college C is given as 5 ∶ 3. The total parts in this ratio are $5 + 3 = 8$.

The number of female students who failed from college C is a fraction of the total failed students in C, determined by this ratio.

Number of female fail students from C = $\frac{\text{Ratio part for Female}}{\text{Total ratio parts}} \times \text{Total failed students in C}$

Number of female fail students from C = $\frac{3}{8} \times 0.9k = \frac{2.7k}{8}$

Determining the Required Ratio

We need to find the ratio between the number of males who passed from B and the number of females who failed from C.

Ratio = (Number of male pass students from B) ∶ (Number of female fail students from C)

Ratio = $\frac{5.5k}{8} : \frac{2.7k}{8}$

We can cancel out the denominator 8 and the constant $k$ from both sides of the ratio:

Ratio = $5.5 : 2.7$

To express this ratio as whole numbers, we can multiply both sides by 10:

Ratio = $5.5 \times 10 : 2.7 \times 10 = 55 : 27$

Based on the data and the given ratio of total students in B and C, the ratio of male students who passed from B to female students who failed from C is 55 ∶ 27.

Looking at the options provided:

1. 2 ∶ 1
2. 1 ∶ 2
3. 55 ∶ 27
4. 27 ∶ 55

Our calculated ratio 55 ∶ 27 matches Option 3. The provided correct answer text is 2 ∶ 1, which corresponds to Option 1.

Revision Table

Additional Information on Ratios and Percentages in Data Interpretation

Data interpretation questions often involve understanding how percentages, ratios, and fractions relate to absolute numbers within a dataset. In problems like this, starting by assuming a variable or a set of convenient numbers for the total quantities is a common and effective strategy. When dealing with ratios of total populations (like students in college B and C), representing them as $2k$ and $3k$ helps maintain the correct proportion while allowing calculations based on percentages and internal ratios. The constant $k$ will cancel out when forming the final ratio, confirming that the specific total number chosen does not affect the final ratio.

It's crucial to correctly identify which ratio (pass or fail) applies to which group (male or female) and to use the corresponding pass or fail percentage when calculating the subgroups. For example, the male:female ratio among *passed* students is applied to the *total passed* students, not the total students in the college.