A man travels at a speed of 20 text{km/hr} and then returns at a speed of 30 text{km/hr}. His average speed of the whole journey is:

Option c: 24 text{km/hr}. Solution: Step 1: Apply the harmonic mean formula for equal distances. text{Average speed} = 2 v1 v2/v1 + v2 Step 2: Substitute values. - v1 = 20 km/hr, v2 = 30 km/hr text{Average speed} = 2 x 20 x 30/20 + 30 = 1200/50 = 24 text{ km/hr} Verification: Let distance = d. Total time = d/20 + d/30 = 3d+2d/60 = d/12. Average speed = 2d/d/12 = 24 km/hr ✓ Hence, Option C is the correct answer.

Central Tendency & DispersionMTP March 21Question 3015 of 473

All Questions

A man travels at a speed of $\displaystyle 20 \text{km/hr}$ and then returns at a speed of $\displaystyle 30 \text{km/hr}$ . His average speed of the whole journey is:

Options

\displaystyle 25 \text{km/hr}

\displaystyle 24.5 \text{km/hr}

\displaystyle 24 \text{km/hr}

DNone

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Correct Answer

✅ Option c — $\displaystyle 24 \text{km/hr}$

All Options:

A $\displaystyle 25 \text{km/hr}$
B $\displaystyle 24.5 \text{km/hr}$
C $\displaystyle 24 \text{km/hr}$
DNone

Detailed Solution & Explanation

**Step 1: Apply the harmonic mean formula for equal distances.**

\text{Average speed} = \frac{2 v_1 v_2}{v_1 + v_2}

**Step 2: Substitute values.** -

\displaystyle v_1 = 20

km/hr,

\displaystyle v_2 = 30

km/hr

\text{Average speed} = \frac{2 \times 20 \times 30}{20 + 30} = \frac{1200}{50} = 24 \text{ km/hr}

**Verification:** Let distance =

\displaystyle d

. Total time =

\displaystyle \frac{d}{20} + \frac{d}{30} = \frac{3d+2d}{60} = \frac{d}{12}

. Average speed =

\displaystyle \frac{2d}{d/12} = 24

km/hr ✓ Hence, **Option C** is the correct answer.

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A man travels at a speed of 20km/hr\displaystyle 20 \text{km/hr}20km/hr and then returns at a speed of 30km/hr\displaystyle 30 \text{km/hr}30km/hr. His average speed of the whole journey is: