Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
(a)35
(b)$36 \frac{2}{3}$
(c)$37 \frac{1}{2}$
(d)40
Answer
Answer (as printed): D
Explanation
Let distance $=x \mathrm{km}$ and usual rate $=y \mathrm{kmph}$. $$\frac{x}{y}-\frac{x}{y+3}=\frac{40}{60} \text { or } 2 y(y+3)=9 x$$ And, $\frac{x}{y-2}-\frac{x}{y}=\frac{40}{60}$ or $y(y-2)=3 x$ On dividing $(i)$ by (ii), we get : $$2(y+3)=3(y-2) \Rightarrow y=12 .$$ ∴ Distance $=x=\frac{2 y(y+3)}{9}=\left(\frac{2 \times 12 \times 15}{9}\right) \mathrm{km}=40 \mathrm{km}$.