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4.Average
hard
The average speed of a train running at a speed of $30\, km / h$ during the first $100\, kilometres,$ at $40\, km / h$ during the second $100\, kilometres$ and at $50\,km / h$ during the last $100\, kilometres$ is nearly (in $km/h$)
A
$38.5$
B
$38.3$
C
$40.0$
D
$39.2$
Solution
Time taken to cover first $100\, kilometres$
$=\frac{100}{30}=3 \frac{1}{3} hrs$
Time taken to cover second $100 \,kilometres$
$=\frac{100}{40}=2 \frac{1}{2} hrs$
Time take to cover last $100 \,kilometres$
$=\frac{100}{50}=2 \,hrs$
Total time taken $=3 \frac{1}{3}+2 \frac{1}{2}+2=\frac{10}{3}+\frac{5}{2}+2$
$=\frac{47}{6} h$
Total distance covered $=300 \,km$
$\therefore \quad$ Average speed $=\frac{300}{47 / 6}=\frac{300 \times 6}{47}=38.3 km / h$
Standard 13
Quantitative Aptitude
