A person travels from A to B at the rate of 20 km/hr and from B to A at the rate of 30 km/hr . What is the average rate of whole journey?

Option b: 24 km/hr. Solution: Step 1: Apply the harmonic mean formula for equal distances. Average speed = 2 v1 v2/v1 + v2 Step 2: Substitute values. - v1 = 20 km/hr, v2 = 30 km/hr Average speed = 2 × 20 × 30/20 + 30 = 1200/50 = 24 km/hr Verification: Let distance AB = d . Total distance = 2d . Total time = d/20 + d/30 = 3d + 2d/60 = 5d/60 = d/12 . Average speed = 2d/d/12 = 24 km/hr ✓ Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 19Question 3012 of 473

All Questions

A person travels from A to B at the rate of $\displaystyle 20 \text{ km/hr}$ and from B to A at the rate of $\displaystyle 30 \text{ km/hr}$ . What is the average rate of whole journey?

Options

\displaystyle 30 \text{ km/hr}

\displaystyle 24 \text{ km/hr}

\displaystyle 35 \text{ km/hr}

DNone of these

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Correct Answer

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

All Options:

A $\displaystyle 30 \text{ km/hr}$
B $\displaystyle 24 \text{ km/hr}$
C $\displaystyle 35 \text{ km/hr}$
DNone of these

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 AB = d

. Total distance

\displaystyle = 2d

. Total time

\displaystyle = \frac{d}{20} + \frac{d}{30} = \frac{3d + 2d}{60} = \frac{5d}{60} = \frac{d}{12}

. Average speed

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

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 person travels from A to B at the rate of 20 km/hr\displaystyle 20 \text{ km/hr}20 km/hr and from B to A at the rate of 30 km/hr\displaystyle 30 \text{ km/hr}30 km/hr. What is the average rate of whole journey?