Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
Two ladies simultaneously leave cities $A$ and $B$ connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches $B$ one hour before the second lady reaches $A$. The two cities $A$ and $B$ are 24 km apart. How many kilometres does each lady travel in one hour?
(a)5 km, 3 km
(b)7 km, 5 km
(c)8 km, 6 km
(d)6 km, 14 km
Answer
Answer (as printed): C
Explanation
Let the speed of the second lady be $x$ km/hr. Then, speed of first lady = $(x + 2)$ km/hr. $$\frac{24}{x}-\frac{24}{x+2}=1 \Rightarrow x(x+2)=48$$ $$\Rightarrow x^2+2x-48=0 \Rightarrow x^2+8x-6x-48=0$$ $$\Rightarrow x(x+8)-6(x+8)=0 \Rightarrow (x+8)(x-6)=0 \Rightarrow x=6.$$ Hence, speed of first lady = 8 km/hr; speed of second lady = 6 km/hr.
Explanation as extracted from the printed page; notation may be imperfect.