The following table gives the percentage of students belonging to low income group in each of the five colleges A, B, C, D and E, along with the proportion of males and females with and without low income.College Name Percentage of students
with low incomeProportion of males
and femalesWith low income Without low income M:F M:F A 35 5:6 6:7 B 25 3:5 4:5 C 24 1:2 2:3 D 19 3:2 4:3 E 15 5:3 3:2
Understanding College Student Data
The question asks to find the college with the fewest female students with low income. We are given that all colleges have the same number of total students. We need to use the provided percentages and ratios.
Let 'T' be the total number of students in each college. Since 'T' is constant across all colleges, we can calculate the number of female students with low income for each college. For simplicity, we can assume T = 100 students per college to easily compare the results.
Calculating Female Students with Low Income
The number of female students with low income is determined by first finding the number of students with low income and then applying the male-to-female ratio for that group.
Formula:
$Number of Females (Low Income) = T * (Percentage Low Income / 100) * (Female Ratio Part / Total Ratio Parts)$
Assuming T = 100:
| College | % Students with Low Income | M:F Ratio (Low Income) | Low Income Students (T=100) | Female Proportion (Low Income) | Female Students with Low Income (T=100) |
| A | 35% | 6:7 | $100 \times \frac{35}{100} = 35$ | $\frac{7}{6+7} = \frac{7}{13}$ | $35 \times \frac{7}{13} \approx 18.85$ |
| B | 25% | 3:5 | $100 \times \frac{25}{100} = 25$ | $\frac{5}{3+5} = \frac{5}{8}$ | $25 \times \frac{5}{8} = 15.625$ |
| C | 24% | 1:2 | $100 \times \frac{24}{100} = 24$ | $\frac{2}{1+2} = \frac{2}{3}$ | $24 \times \frac{2}{3} = 16$ |
| D | 19% | 3:2 | $100 \times \frac{19}{100} = 19$ | $\frac{2}{3+2} = \frac{2}{5}$ | $19 \times \frac{2}{5} = 7.6$ |
| E | 15% | 5:3 | $100 \times \frac{15}{100} = 15$ | $\frac{3}{5+3} = \frac{3}{8}$ | $15 \times \frac{3}{8} = 5.625$ |
Comparing Results for Low Income Females
After calculating the number of female students with low income for each college (assuming T=100), we compare the values:
- College A: $\approx 18.85$
- College B: $15.625$
- College C: $16$
- College D: $7.6$
- College E: $5.625$
The smallest value among these represents the college with the least number of female students with low income.
Important Questions from Tabulation
What is the ratio of total number of patients recovered from covid-19 in April to total number of patients recovered from covid-19 in March?
In which state, the number of patients who recovered from covid-19 steadily decreasing?
What is the average number of patients who recovered from Covid-19 in Madhya Pradesh in four months?
Find the difference between the total number of patients recovered from Covid-19 in all months in Punjab and the total number of patients recovered from Covid-19 in all months in Rajasthan.
In February 2021 the number of patients recovered from Covid-19 in Punjab is how much approximant percent more/less than the number of patients recovered from Covid-19 Uttar Pradesh in the same month?
