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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Determinants

NDA 2018 · Mathematics · Determinants

A train covers the first 5 km of its journey at a speed of 30 km /...

A train covers the first 5 km of its journey at a speed of 30 km/hr\mathrm{km} / \mathrm{hr} and the next 15 km at a speed of 45km/hr45 \mathrm{ km} / \mathrm{hr}. What is the average speed of the train?

Options

  1. A35km/hr35 \mathrm{ km} / \mathrm{hr}
  2. B37.5km/hr37.5 \mathrm{ km} / \mathrm{hr}
  3. C39.5km/hr39.5 \mathrm{ km} / \mathrm{hr}
  4. D40km/hr40 \mathrm{ km} / \mathrm{hr}

Correct answer

D. 40km/hr40 \mathrm{ km} / \mathrm{hr}

Step-by-step solution

Time taken by train to cover first 5km= Distance  Speed =530=16hrTimetakenbytrain5 \mathrm{ km}=\frac{\text{ Distance }}{\text{ Speed }}=\frac{5}{30}=\frac{1}{6} \mathrm{hr} Time taken by train to cover next15 km=1545=13hr\mathrm{ km}=\frac{15}{45}=\frac{1}{3} \mathrm{hr}.  Average speed =5+1516+13=201+26=1203=40km/hr\begin{aligned} & \text{ Average speed }=\frac{5+15}{\frac{1}{6}+\frac{1}{3}} \\ & =\frac{20}{\frac{1+2}{6}}=\frac{120}{3}=40 \mathrm{ km} / \mathrm{hr} \end{aligned}
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