In a college, class A has 25 students and class B has 30 stude... | Mathematics MCQ | Examoogle

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MathematicsPercentage

In a college, class A has 25 students and class B has 30 students. If the number of students in class A increases by 20% in the first year and by 10% in the second year, and the number of students in class B increases by a total of 20% in two years, what is the overall percentage increase in the total number of students in the college over the two years? (Give your answer rounded off to 2 decimal places.)

20.85%

20.45%

25.45%

25.85%

Correct Answer

📐 MA • Math Weighted Average MethodMathematicsPercentage

Option C

25.45%

Quick Summary:

Calculate the final number of students for each class independently: Class A final = $25 \times 1.20 \times 1.10 = 33$ ; Class B final = $30 \times 1.20 = 36$ . Sum = $33 + 36 = 69$ .

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📐MAMath SolutionWeighted Average Method

📋 Given

Class A initial students = 25, Class B initial students = 30. Class A growth = 20% then 10%. Class B total growth = 20%.

🔢 Formula Used

Total Percentage=Final Total−Initial TotalInitial Total×100\text{Total}\ \text{Percentage} = \frac{\text{Final}\ \text{Total} - \text{Initial}\ \text{Total}}{\text{Initial}\ \text{Total}} \times 100Total Percentage=Initial TotalFinal Total−Initial Total​×100

⚡ Exam Hall Shortcut / Speed Trick

Calculate the final number of students for each class independently: Class A final = $25 \times 1.20 \times 1.10 = 33$ ; Class B final = $30 \times 1.20 = 36$ . Sum = $33 + 36 = 69$ .

⚠️ Common Student Trap / Pitfall

Students often wrongly calculate Class A growth by adding the percentages (20% + 10% = 30%) instead of using successive percentage increase (compound growth).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate final students in Class A

Successive growth of 20% and 10% on 25 students: $25 \times (1 + 0.20) \times (1 + 0.10)$ .

25×1.2×1.1=3325 \times 1.2 \times 1.1 = 3325×1.2×1.1=33

Calculate final students in Class B

A total increase of 20% on 30 students: $30 \times (1 + 0.20)$ .

30×1.2=3630 \times 1.2 = 3630×1.2=36

Determine total increase

Total initial students = $25 + 30 = 55$ . Total final students = $33 + 36 = 69$ . Increase = $69 - 55 = 14$ .

Percentage Increase=1455×100\text{Percentage}\ \text{Increase} = \frac{14}{55} \times 100Percentage Increase=5514​×100

Calculate final percentage

Performing the final division: $1400 / 55 \approx 25.4545...$

25.45%25.45\%25.45%

✅

C is correct because the total number of students increased from 55 to 69, resulting in a percentage increase of 25.45%.

Core Concepts Used

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Successive Percentage Change Weighted Average Arithmetic Growth

💡 EXAM TIP

Successive percentage increases are identical to the logic of Compound Interest ( $A = P(1 + r/100)^n$ ); always remember to apply growth factors multiplicatively.

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