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 ?
Correct Answer: 100 km/hr, 80 km/hr
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
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