Subject: General Aptitude · Chapter: Time and Distance · Exam: 2006 · Marks: · Difficulty:
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 speeds 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/ 100 km/hr, 90 km/ hr hr
Answer
Answer (as printed): B
Explanation
Let the speeds of the train and the car be $x \mathrm{km} / \mathrm{hr}$ and $y \mathrm{km} / \mathrm{hr}$ respectively. Then, $$\frac{160}{x}+\frac{600}{y}=8 \Rightarrow \frac{20}{x}+\frac{75}{y}=1$$ And, $$\frac{240}{x}+\frac{520}{y}=8 \frac{1}{5} \Rightarrow \frac{240}{x}+\frac{520}{y}=\frac{41}{5}$$ Multiplying (i) by 12 and subtracting (ii) from it, we get : $$\frac{380}{y}=12-\frac{41}{5}=\frac{19}{5} \Rightarrow y=\left(380 \times \frac{5}{19}\right)=100 .$$ Putting $y=100$ in (i), we get : $\frac{20}{x}+\frac{3}{4}=1 \Rightarrow \frac{20}{x}=\frac{1}{4} \Rightarrow x=80$. Hence, speed of car $=100 \mathrm{km} / \mathrm{hr}$, speed of train $=80 \mathrm{km} / \mathrm{hr}$