Subject: General Aptitude · Chapter: Time and Distance · Exam: 2005 · Marks: · Difficulty:
A walks at a uniform rate of 4 km an hour; and 4 hours after his start, $B$ bicycles after him at the uniform rate of 10 km an hour. How far from the starting point will B catch A?
(a)16.7 km
(b)18.6 km
(c)21.5 km
(d)26.7 km
Answer
Answer (as printed): D
Explanation
Distance covered by $A$ in 4 hrs $=(4 \times 4) \mathrm{km}=16 \mathrm{km}$. Relative speed of $B$ w.r.t. $\mathrm{A}=(10-4) \mathrm{km} / \mathrm{hr}=6 \mathrm{km} / \mathrm{hr}$. Time taken to cover 16 km at relative speed $$=\left(\frac{16}{6}\right) \mathrm{hrs}=\frac{8}{3} \mathrm{hrs} .$$ Distance covered by B in $\frac{8}{3} \mathrm{hrs}=\left(10 \times \frac{8}{3}\right) \mathrm{km}=\left(\frac{80}{3}\right) \mathrm{km}$ $$=26.7 \mathrm{km} .$$