Measures of Central Tendency and DispersionPYQ May 25Question 4369 of 473
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A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

Options

A600 km/hr.
B583.33 km/hr.
C10035\displaystyle 100\sqrt{35} km/hr.
D620 km/hr.
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Correct Answer

✅ Option b — 583.33 km/hr.

All Options:

  • A600 km/hr.
  • B583.33 km/hr.
  • C10035\displaystyle 100\sqrt{35} km/hr.
  • D620 km/hr.

Detailed Solution & Explanation

To find the average speed when covering the same distance at two different speeds, we must use the Harmonic Mean (H.M.) of the speeds:
Let:
- Speed from A to B be v1=500 km/hr\displaystyle v_1 = 500\text{ km/hr}.
- Speed from B to A be v2=700 km/hr\displaystyle v_2 = 700\text{ km/hr}.

The Harmonic Mean of two values v1\displaystyle v_1 and v2\displaystyle v_2 is given by:
Average Speed=21v1+1v2=2v1v2v1+v2\text{Average Speed} = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}} = \frac{2 v_1 v_2}{v_1 + v_2} Substituting the values:
Average Speed=2×500×700500+700\text{Average Speed} = \frac{2 \times 500 \times 700}{500 + 700} Average Speed=700,0001200=700012≈583.33 km/hr\text{Average Speed} = \frac{700,000}{1200} = \frac{7000}{12} \approx 583.33\text{ 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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