Analysing Student Data and Percentage Increase

The question asks us to determine which college among P, Q, R, S, and T experienced the maximum percentage increase in the number of students from the year 2016 to 2021. The provided table gives the number of students admitted (A) and left (L) each year for these five colleges, starting from their foundation year in 2016.

Understanding the College Student Data Table

The table below presents the year-wise student admission and leaving data for colleges P, Q, R, S, and T from 2016 to 2021.

Calculating Students in 2016

Since the year 2016 is the foundation year, the number of students in each college at the end of 2016 is simply the number of students admitted in that year, as no students left in the foundation year.

• College P: 2250 students
• College Q: 2100 students
• College R: 2400 students
• College S: 3200 students
• College T: 3100 students

Calculating Students in 2021

To find the number of students in 2021, we need to consider the cumulative effect of admissions and students leaving each year from 2017 to 2021. The net change in students each year is the number of students admitted minus the number of students who left ($ \text{Net Change} = \text{Admitted} - \text{Left} $).

The total number of students in 2021 for a college is the initial number of students in 2016 plus the sum of the net changes from 2017 to 2021.

$\text{Students in 2021} = \text{Students in 2016} + \sum_{Year=2017}^{2021} (\text{Admitted}_{Year} - \text{Left}_{Year})$

Let's calculate the net change for each college for the years 2017-2021:

Now, let's calculate the total net change from 2017 to 2021 and the total number of students in 2021 for each college:

• College P:
  • Total Net Change (2017-2021) = $220 + 160 + 290 + 260 + 240 = 1170$
  • Students in 2021 = Students in 2016 + Total Net Change = $2250 + 1170 = 3420$
• College Q:
  • Total Net Change (2017-2021) = $400 + 220 + 150 + 220 + 240 = 1230$
  • Students in 2021 = Students in 2016 + Total Net Change = $2100 + 1230 = 3330$
• College R:
  • Total Net Change (2017-2021) = $380 + 300 + 270 + 200 + 260 = 1410$
  • Students in 2021 = Students in 2016 + Total Net Change = $2400 + 1410 = 3810$
• College S:
  • Total Net Change (2017-2021) = $380 + 280 + 350 + 390 + 440 = 1840$
  • Students in 2021 = Students in 2016 + Total Net Change = $3200 + 1840 = 5040$
• College T:
  • Total Net Change (2017-2021) = $250 + 300 + 380 + 460 + 420 = 1810$
  • Students in 2021 = Students in 2016 + Total Net Change = $3100 + 1810 = 4910$

Calculating Percentage Increase in Student Numbers

The percentage increase is calculated using the formula:

$\text{Percentage Increase} = \frac{(\text{Students in 2021} - \text{Students in 2016})}{\text{Students in 2016}} \times 100\%$

Let's calculate the percentage increase for each college:

• College P:
  • Increase = $3420 - 2250 = 1170$
  • Percentage Increase = $\frac{1170}{2250} \times 100\% = \frac{117}{225} \times 100\% = \frac{13 \times 9}{25 \times 9} \times 100\% = \frac{13}{25} \times 100\% = 13 \times 4\% = 52\%$
• College Q:
  • Increase = $3330 - 2100 = 1230$
  • Percentage Increase = $\frac{1230}{2100} \times 100\% = \frac{123}{210} \times 100\% = \frac{41 \times 3}{70 \times 3} \times 100\% = \frac{41}{70} \times 100\% \approx 58.57\%$
• College R:
  • Increase = $3810 - 2400 = 1410$
  • Percentage Increase = $\frac{1410}{2400} \times 100\% = \frac{141}{240} \times 100\% = \frac{47 \times 3}{80 \times 3} \times 100\% = \frac{47}{80} \times 100\% = 0.5875 \times 100\% = 58.75\%$
• College S:
  • Increase = $5040 - 3200 = 1840$
  • Percentage Increase = $\frac{1840}{3200} \times 100\% = \frac{184}{320} \times 100\% = \frac{23 \times 8}{40 \times 8} \times 100\% = \frac{23}{40} \times 100\% = 0.575 \times 100\% = 57.5\%$
• College T:
  • Increase = $4910 - 3100 = 1810$
  • Percentage Increase = $\frac{1810}{3100} \times 100\% = \frac{181}{310} \times 100\% \approx 58.39\%$

Identifying the Maximum Percentage Increase

Let's compare the percentage increases calculated for each college:

• College P: 52%
• College Q: 58.57%
• College R: 58.75%
• College S: 57.5%
• College T: 58.39%

Comparing these values, the maximum percentage increase in the number of students from 2016 to 2021 is approximately 58.75%, which corresponds to College R.

Revision Table: College Student Growth Analysis

From the revision table, it is clear that College R has the maximum percentage increase in students from 2016 to 2021.

Additional Information on Percentage Change Calculations

Percentage change is a useful metric to understand relative growth or decline over time. It is important to use the initial value as the denominator in the calculation. The formula $\frac{\text{Final} - \text{Initial}}{\text{Initial}} \times 100\%$ gives the percentage increase when the final value is greater than the initial value, and the percentage decrease when the final value is less than the initial value (resulting in a negative percentage). In this problem, we calculated percentage increase as the number of students grew in all colleges.