Ramesh travels 760 km to his home, partly by train and partly by car. He takes 8 hours, if he travels 160 km by train and the rest by car. He takes 12 minutes more, if he travels 240 km by train and the rest by car. What are the spends of the car and the train respectively ?
A. 90 km/hr, 60 km/hr
B. 100 km/hr, 80 km/hr
C. 80 km/hr, 70 km/hr
D. 100 km/hr, 90 km/hr
Answer: Option B
Solution(By Examveda Team)
Let the speeds of the train and the car be x km/hr and y km/hr respectively.Then,
$$\eqalign{ & \Rightarrow \frac{{160}}{x} + \frac{{600}}{y} = 8 \cr & \Rightarrow \frac{{20}}{x} + \frac{{75}}{y} = 1.....(i) \cr} $$
And,
$$\eqalign{ & \Rightarrow \frac{{240}}{x} + \frac{{520}}{y} = 8\frac{1}{5} \cr & \Rightarrow \frac{{240}}{x} + \frac{{520}}{y} = \frac{{41}}{5}.....(ii) \cr} $$
Multiplying (i) by 12 and subtracting (ii) from it, we get :
$$\eqalign{ & \Rightarrow \frac{{380}}{y} = 12 - \frac{{41}}{5} \cr & \Rightarrow \frac{{380}}{y} = \frac{{19}}{5} \cr & \Rightarrow y = \left( {380 \times \frac{5}{{19}}} \right) \cr & \Rightarrow y = 100 \cr} $$
Putting y = 100 in equation (i), we get :
$$\eqalign{ & \Rightarrow \frac{{20}}{x} + \frac{3}{4} = 1 \cr & \Rightarrow \frac{{20}}{x} = \frac{1}{4} \cr & \Rightarrow x = 80 \cr} $$
∴ 100 km/hr, 80 km/hr
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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