Subject: General Aptitude · Chapter: Time and Distance · Exam: 2006 · Marks: · Difficulty:
A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster, then it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr, then the train would have taken 6 hours more than the scheduled time. The length of the journey is
(a)700 km
(b)720 km
(c)740 km
(d)760 km
Answer
Answer (as printed): B
Explanation
Let distance $=x \mathrm{km}$ and usual speed $=y \mathrm{kmph}$. $$\frac{x}{y}-\frac{x}{y+6}=4 \Rightarrow 6 x=4 y(y+6)$$ And, $\frac{x}{y-6}-\frac{x}{y}=6 \Rightarrow 6 x=6 y(y-6)$ From (i) and (ii), we get : $4 y(y+6)=6 y(y-6) \Rightarrow 2(y+6)=3(y-6) \Rightarrow y=30$. ∴ Length of the journey $=x=\frac{4 y(y+6)}{6}=\left(\frac{4 \times 30 \times 36}{6}\right) \mathrm{km}$