In a college, class X has 40 students and class Y has 60 stude... | Mathematics MCQ | Examoogle

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In a college, class X has 40 students and class Y has 60 students. If the number of students in class X increases by 10% in the first year and by 20% in the second year, and the number of students in class Y increases by a total of 15% in two years, what is the overall percentage increase in the total number of students in the college? (Round to 2 decimal places)

16.20%

17.40%

18.50%

19.10%

Correct Answer

📐 MA • Math Weighted Average MethodMathematicsPercentage

Option A

16.20%

Quick Summary:

Use the formula for successive percentage change $A+B+\frac{AB}{100}$ for Class X, which is $10+20+\frac{10 \times 20}{100} = 32\%$ , then take the weighted average: $\frac{40 \times 32 + 60 \times 15}{100}$ .

📐MAMath SolutionWeighted Average Method

📋 Given

Class X has 40 students with successive increases of 10% and 20%. Class Y has 60 students with a total increase of 15%. Total initial students = 100.

🔢 Formula Used

Overall Increase=(Increase in X+Increase in Y)Total Students×100%\text{Overall Increase} = \frac{(\text{Increase in X} + \text{Increase in Y})}{\text{Total Students}} \times 100\%Overall Increase=Total Students(Increase in X+Increase in Y)​×100%

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often add the percentages directly ( $10+20+15 = 45$ divided by 3) instead of applying the compound increase to Class X first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total increase in Class X

Since Class X experiences successive increases of 10% and 20%, the total percentage increase is calculated using the formula $x + y + \frac{xy}{100}$ .

10+20+10×20100=32%10 + 20 + \frac{10 \times 20}{100} = 32\%10+20+10010×20​=32%

Calculate absolute increase for both classes

Number of new students in X is $40 \times 32\% = 12.8$ . Number of new students in Y is $60 \times 15\% = 9$ .

Total new students=12.8+9=21.8\text{Total new students} = 12.8 + 9 = 21.8Total new students=12.8+9=21.8

Calculate overall percentage increase

The total initial students were $40 + 60 = 100$ . The overall percentage increase is the total increase divided by the total initial students.

21.8100×100=16.20%\frac{21.8}{100} \times 100 = 16.20\%10021.8​×100=16.20%

✅

A is correct because the weighted average of the percentage increases $(40 \times 32\% + 60 \times 15\%) / 100$ results in an overall increase of 16.20%.

Core Concepts Used

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Successive Percentage Change Weighted Average Base Value Calculation

💡 EXAM TIP

This weighted average logic is frequently used in Mixture and Alligation problems where you balance concentrations or percentage changes across different group sizes.

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