Subject: General Aptitude · Chapter: Time and Distance · Exam: 2004 · Marks: · Difficulty:
$A$ and $B$ start from the same point and in the same direction at 7 a.m. to walk around a rectangular field $400 \mathrm{m} \times 300 \mathrm{m}$. $A$ and $B$ walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 12 : 30 p.m.?
(a)Not even once
(b)Once
(c)Twice
(d)Thrice
Answer
Answer (as printed): B
Explanation
Perimeter of the field $=2(400+300) \mathrm{m}=1400 \mathrm{m}=1.4 \mathrm{km}$. Since A and B move in the same direction, so they will first meet each other when there is a difference of one round i.e., 1.4 km between the two. Relative speed of $A$ and $B=(3-2.5) \mathrm{km} / \mathrm{hr}=0.5 \mathrm{km} / \mathrm{hr}$. Time take to cover 1.4 km at this speed $=\left(\frac{1.4}{0.5}\right) \mathrm{hr}$ $$=2 \frac{4}{5} \mathrm{hr}=2 \mathrm{hr} 48 \mathrm{min} .$$ So they shall first cross each other at 9 : 48 a.m. and again, 2 hr 48 min after 9 : 48 a.m. i.e., 12 : 36 p.m. Thus, till 12 : 30 p.m. they will cross each other once.