A man travels from Delhi to Agra at an average speed of $30 km per hour and back at an average speed of $60 km per hour . What's the average speed.

Option b: $40 km/hr$. Solution: Step 1: Identify the appropriate formula. For a round trip covering equal distances at two different speeds, the average speed is the Harmonic Mean of the two speeds: Average speed = 2 v1 v2/v1 + v2 Step 2: Substitute values. - v1 = 30 km/hr - v2 = 60 km/hr Average speed = 2 × 30 × 60/30 + 60 = 3600/90 = 40 km/hr Verification via time-distance method: Let distance = d km. - Time for Delhi to Agra = d/30 hours - Time for return = d/60 hours - Total distance = $2d$ - Total time = d/30 + d/60 = 2d/60 + d/60 = 3d/60 = d/20 - Average speed = $2d ÷ (d/20) = 40$ km/hr ✓ Hence, Option B is the correct answer.

A man travels from Delhi to Agra at an average speed of $30 km per hour and back at an average speed of $60 km per hour . What's the average speed.

The correct answer is Option b: $40 km/hr$. Step 1: Identify the appropriate formula. For a round trip covering equal distances at two different speeds, the average speed is the Harmonic Mean of the two speeds: Average speed = 2 v1 v2/v1 + v2 Step 2: Substitute values. - v1 = 30 km/hr - v2 = 60 km/hr Average speed = 2 × 30 × 60/30 + 60 = 3600/90 = 40 km/hr Verification via time-distance method: Let distance = d km. - Time for Delhi to Agra = d/30 hours - Time for return = d/60 hours - Total distance = $2d$ - Total time = d/30 + d/60 = 2d/60 + d/60 = 3d/60 = d/20 - Average speed = $2d ÷ (d/20) = 40$ km/hr ✓ Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP May 18Question 3010 of 473

All Questions

A man travels from Delhi to Agra at an average speed of $30 $\displaystyle \text{km per hour}<span$ class="katex-error" title="ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 47: …erage speed of &̲#36;60 \text{km…" style="color:#cc0000">\displaystyle and back at an average speed of $60 $\displaystyle \text{km per hour}$ . What's the average speed.

Select Your Answer (Keyboard: A, B, C, D)

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $40 \text{ km/hr}$

All Options:

A$48 \text{ km/hr}$
B$40 \text{ km/hr}$
C$45 \text{ km/hr}$
D$35 \text{ km/hr}$

Detailed Solution & Explanation

**Step 1: Identify the appropriate formula.** For a round trip covering equal distances at two different speeds, the average speed is the **Harmonic Mean** of the two speeds:

Average speed = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}

**Step 2: Substitute values.** -

\displaystyle v_1 = 30

km/hr -

\displaystyle v_2 = 60

km/hr

Average speed = \frac{2 \times 30 \times 60}{30 + 60} = \frac{3600}{90} = 40 km/hr

**Verification via time-distance method:** Let distance =

\displaystyle d

km. - Time for Delhi to Agra =

\displaystyle d/30

hours - Time for return =

\displaystyle d/60

hours - Total distance = $2d$ - Total time =

\displaystyle d/30 + d/60 = 2d/60 + d/60 = 3d/60 = d/20

- Average speed = $2d

\displaystyle \div

(d/20) = 40$ km/hr ✓ Hence, **Option B** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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