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 $30 \text{km per hour}$ and back at an average speed of $60 \text{km per hour}$. What's the average speed.

The correct answer is Option b: $40 \text{ km/hr}$. **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: $$\text{Average speed} = \frac{2 v_1 v_2}{v_1 + v_2}$$ **Step 2: Substitute values.** - $v_1 = 30$ km/hr - $v_2 = 60$ km/hr $$\text{Average speed} = \frac{2 \times 30 \times 60}{30 + 60} = \frac{3600}{90} = 40 \text{ km/hr}$$ **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 = $2d \div (d/20) = 40$ 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 $\displaystyle 30 \text{km per hour}$ and back at an average speed of $\displaystyle 60 \text{km per hour}$ . What's the average speed.

Options

\displaystyle 48 \text{ km/hr}

\displaystyle 40 \text{ km/hr}

\displaystyle 45 \text{ km/hr}

\displaystyle 35 \text{ km/hr}

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

Correct Answer

✅ Option b — $\displaystyle 40 \text{ km/hr}$

All Options:

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

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:

\text{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

\text{Average speed} = \frac{2 \times 30 \times 60}{30 + 60} = \frac{3600}{90} = 40 \text{ 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 =

\displaystyle 2d

- Total time =

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

- Average speed =

\displaystyle 2d \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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A man travels from Delhi to Agra at an average speed of 30km per hour\displaystyle 30 \text{km per hour}30km per hour and back at an average speed of 60km per hour\displaystyle 60 \text{km per hour}60km per hour. What's the average speed.