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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Sequences and Series

NDA 2019 · Mathematics · Sequences and Series

A car travels first 60 km at a speed of 3 v km / hr and travels...

A car travels first 60 km at a speed of 3vkm/hr3 \mathrm{v} \mathrm{km} / \mathrm{hr} and travels next 60 km at 2vkm/hr2 \mathrm{v} \mathrm{km} / \mathrm{hr}. What is the average speed of the car?

Options

  1. A2.5vkm/hr2.5 \mathrm{vkm} / \mathrm{hr}
  2. B2.4vkm/hr2.4 \mathrm{vkm} / \mathrm{hr}
  3. C2.2vkm/hr2.2 \mathrm{vkm} / \mathrm{hr}
  4. D2.1vkm/hr2.1 \mathrm{vkm} / \mathrm{hr}

Correct answer

B. 2.4vkm/hr2.4 \mathrm{vkm} / \mathrm{hr}

Step-by-step solution

For first 60 km , speed =3vkmph=3 v \mathrm{kmph} for next 60 km speed =2vkmph=2 v \mathrm{kmph} avg. speed = Total distance  Total time =120603v+60v=213v+12v=2v5×6=12v5=2.4vkmph\begin{aligned} & \text{ avg. speed }=\frac{\text{ Total distance }}{\text{ Total time }} \\ & =\frac{120}{\frac{60}{3 v}+\frac{60}{v}} \\ & =\frac{2}{\frac{1}{3 v}+\frac{1}{2 v}} \\ & =\frac{2 v}{5} \times 6 \\ & =\frac{12 v}{5}=2.4 \mathrm{vkmph} \end{aligned}$$
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