Central Tendency & DispersionMTP Nov 19Question 3012 of 473
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A person travels from A to B at the rate of 20 km/hr\displaystyle 20 \text{ km/hr} and from B to A at the rate of 30 km/hr\displaystyle 30 \text{ km/hr}. What is the average rate of whole journey?

Options

A30 km/hr\displaystyle 30 \text{ km/hr}
B24 km/hr\displaystyle 24 \text{ km/hr}
C35 km/hr\displaystyle 35 \text{ km/hr}
DNone of these
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Correct Answer

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

All Options:

  • A30 km/hr\displaystyle 30 \text{ km/hr}
  • B24 km/hr\displaystyle 24 \text{ km/hr}
  • C35 km/hr\displaystyle 35 \text{ km/hr}
  • DNone of these

Detailed Solution & Explanation

**Step 1: Apply the harmonic mean formula for equal distances.** Average speed=2v1v2v1+v2\text{Average speed} = \frac{2 v_1 v_2}{v_1 + v_2} **Step 2: Substitute values.** - v1=20\displaystyle v_1 = 20 km/hr, v2=30\displaystyle v_2 = 30 km/hr Average speed=2×20×3020+30=120050=24 km/hr\text{Average speed} = \frac{2 \times 20 \times 30}{20 + 30} = \frac{1200}{50} = 24 \text{ km/hr} **Verification:** Let distance AB=d\displaystyle AB = d. Total distance =2d\displaystyle = 2d. Total time =d20+d30=3d+2d60=5d60=d12\displaystyle = \frac{d}{20} + \frac{d}{30} = \frac{3d + 2d}{60} = \frac{5d}{60} = \frac{d}{12}. Average speed =2dd/12=24\displaystyle = \frac{2d}{d/12} = 24 km/hr ✓ Hence, **Option B** is the correct answer.

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