Find the total number of participants in marathon in 2026, if ... | Mathematics MCQ | Examoogle

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MathematicsArithmetic

Find the total number of participants in marathon in 2026, if the total participants i increased by 25% in 2026 over the average of participants in 2024 and 2025.

3700

3775

3800

3875

None of the above

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic

Option D

3875

Quick Summary:

Calculate the average of 3000 and 3200 as 3100. Then, find 125% of 3100: $3100 + 775 = 3875$ .

📐MAMath SolutionDirect Formula

📋 Given

Participants in 2024: 3000 (1500 male + 1500 female), Participants in 2025: 3200 (1600 male + 1600 female). Percentage increase for 2026: 25% over average.

🔢 Formula Used

Average2024,2025=P2024+P20252,P2026=Average2024,2025×(1+0.25)\text{Average}_{2024, 2025} = \frac{P_{2024} + P_{2025}}{2}, \quad P_{2026} = \text{Average}_{2024, 2025} \times (1 + 0.25)Average2024,2025​=2P2024​+P2025​​,P2026​=Average2024,2025​×(1+0.25)

⚡ Exam Hall Shortcut / Speed Trick

Calculate the average of 3000 and 3200 as 3100. Then, find 125% of 3100: $3100 + 775 = 3875$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the increase on each year separately or misunderstand 'over the average', leading to incorrect summation.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total participants for 2024 and 2025

From the bar graph, 2024 has 1500 males and 1500 females, total $1500 + 1500 = 3000$ . 2025 has 1600 males and 1600 females, total $1600 + 1600 = 3200$ .

Total2024=3000,Total2025=3200\text{Total}_{2024} = 3000, \quad \text{Total}_{2025} = 3200Total2024​=3000,Total2025​=3200

Find the average of participants in 2024 and 2025

The average is the sum of participants divided by 2.

Average=3000+32002=3100\text{Average} = \frac{3000 + 3200}{2} = 3100Average=23000+3200​=3100

Calculate the participants for 2026

The total participants increased by 25% over the average calculated.

P2026=3100×(1+0.25)=3100×1.25=3875P_{2026} = 3100 \times (1 + 0.25) = 3100 \times 1.25 = 3875P2026​=3100×(1+0.25)=3100×1.25=3875

✅

D is correct because the average of participants in 2024 and 2025 is 3100, and a 25% increase results in 3875.

Core Concepts Used

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Arithmetic Average Percentage Increase Data Interpretation

💡 EXAM TIP

Always identify the base value for percentage increases carefully; here it is specifically the 'average' of the two preceding years, not the previous single year.

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