Central Tendency & DispersionMTP May 18Question 3010 of 473
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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} and back at an average speed of 60km per hour\displaystyle 60 \text{km per hour}. What's the average speed.

Options

A48 km/hr\displaystyle 48 \text{ km/hr}
B40 km/hr\displaystyle 40 \text{ km/hr}
C45 km/hr\displaystyle 45 \text{ km/hr}
D35 km/hr\displaystyle 35 \text{ km/hr}
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Correct Answer

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

All Options:

  • A48 km/hr\displaystyle 48 \text{ km/hr}
  • B40 km/hr\displaystyle 40 \text{ km/hr}
  • C45 km/hr\displaystyle 45 \text{ km/hr}
  • D35 km/hr\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: Average speed=2v1v2v1+v2\text{Average speed} = \frac{2 v_1 v_2}{v_1 + v_2} **Step 2: Substitute values.** - v1=30\displaystyle v_1 = 30 km/hr - v2=60\displaystyle v_2 = 60 km/hr Average speed=2×30×6030+60=360090=40 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\displaystyle d km. - Time for Delhi to Agra = d/30\displaystyle d/30 hours - Time for return = d/60\displaystyle d/60 hours - Total distance = 2d\displaystyle 2d - Total time = d/30+d/60=2d/60+d/60=3d/60=d/20\displaystyle d/30 + d/60 = 2d/60 + d/60 = 3d/60 = d/20 - Average speed = 2d÷(d/20)=40\displaystyle 2d \div (d/20) = 40 km/hr ✓ Hence, **Option B** is the correct answer.

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