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MathematicsArithmetic Aptitude

A person travels 10km at 20km/h and 10km at 30km/h · What is the average speed?

24 $\text{ km/h}$

25 $\text{ km/h}$

22 $\text{ km/h}$

26 $\text{ km/h}$

Correct Answer

⚙️ TE • Technical Harmonic Mean MethodMathematicsArithmetic Aptitude

Option A

24 $\text{ km/h}$

Quick Summary:

Given: Distance 1 (d1) = 10km, Speed 1 (s1) = 20km/h; Distance 2 (d2) = 10km, Speed 2 (s²) = 30km/h.

📐MAMath SolutionHarmonic Mean Method

📋 Given

Distance 1 (d1) = 10km, Speed 1 (s1) = 20km/h; Distance 2 (d2) = 10km, Speed 2 (s²) = 30km/h.

🔢 Formula Used

Vavg=2×s1×s2s1+s2V_{avg} = \frac{2 \times s_1 \times s_2}{s_1 + s_2}Vavg​=s1​+s2​2×s1​×s2​​

⚡ Exam Hall Shortcut / Speed Trick

Since the distances are equal, use the harmonic mean formula: $2xy / (x+y)$ , where $x=20$ and $y=30$ . This avoids calculating total time manually.

⚠️ Common Student Trap / Pitfall

Most students calculate the simple arithmetic mean (20+30)/2 = 25 km/h, which is incorrect for average speed over equal distances.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the given speeds

Given speeds are $s_1 = 20$ km/h and $s_2 = 30$ km/h over equal distances.

s1=20,s2=30s_1 = 20, s_2 = 30s1​=20,s2​=30

Apply Harmonic Mean formula

Since distance is equal, the average speed is the harmonic mean of the two speeds.

Vavg=2×20×3020+30V_{avg} = \frac{2 \times 20 \times 30}{20 + 30}Vavg​=20+302×20×30​

Calculate the result

Simplify the numerator to $1200$ and the denominator to $50$ .

Vavg=120050=24 km/hV_{avg} = \frac{1200}{50} = 24 \text{ km/h}Vavg​=501200​=24 km/h

✅

A is correct because the average speed calculated using the harmonic mean formula $2xy/(x+y)$ is 24 km/h.

Core Concepts Used

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💡 EXAM TIP

This harmonic mean shortcut is extremely useful in Work and Time problems where two people complete the same task at different rates.

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