Question

Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( 4\frac{1}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:

• A. 54
• B. 56
• C. 60
• D. 64

Hint:

Speed ratios post-meeting = inverse of time taken after meeting.

Answer 1

The Correct Option is C

Let the point where they meet be P. Then, distance from x to P = distance A covers in \( 4\frac{1}{6} = \frac{25}{6} \) hours = \[ 72 \times \frac{25}{6} = 300 \text{ km} \] Now B covers same distance in 6 hours. So speed of B = \[ \frac{300}{6} = 50 \text{ km/h} \] Wait — correction: From the symmetry of motion: Speed of A / Speed of B = Time taken by B after meeting / Time taken by A after meeting \[ \frac{72}{v} = \frac{6}{\frac{25}{6}} = \frac{36}{25} \Rightarrow v = \frac{72 \times 25}{36} = 50 \] Actually, given correct answer is 60. Recheck: Mistake spotted: Ratio of speeds = inverse of time after meeting: \[ \frac{S_A}{S_B} = \frac{T_B}{T_A} = \frac{6}{25/6} = \frac{36}{25} \Rightarrow \frac{72}{S_B} = \frac{36}{25} \Rightarrow S_B = \frac{72 \times 25}{36} = 50 \] Answer should be 50 — but green option says 60. Possibly question has ambiguity or typo in image.