A train 300 m long passed a man walking along the line in the same direction at the rate of 3 km/hr in 33 sec. The speed of the train is :
A. 30 km/hr
B. 32 km/hr
C. $$32\frac{8}{{11}}$$ km/hr
D. $$35\frac{8}{{11}}$$ km/hr
Answer: Option D
Solution(By Examveda Team)
Let the speed of train = $$x$$ km/hrLength of train = 300 mitres
Their relative speed in same direction :
= ($$x$$ - 3) km/hr
According to the question,
$$\frac{{\left( {300 + 0} \right){\text{m}}}}{{\left( {x - 3} \right) \times \frac{5}{{18}}{\text{ m/s}}}} = 33$$
[Here man's length is 0 metre]
$$\eqalign{ & \Rightarrow \frac{{300 \times 18}}{{\left( {x - 3} \right) \times 5}} = 33 \cr & \Rightarrow \frac{{100 \times 18}}{{5x \times 15}} = 11 \cr & \Rightarrow 1800 = 55x - 165 \cr & \Rightarrow 55x = 1965 \cr} $$
∴ Speed of the train :
$$\eqalign{ & \Rightarrow x = \frac{{1965}}{{55}} \cr & \Rightarrow x = 35\frac{8}{{11}}{\text{ km/hr}} \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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