Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.  Choose the most appropriate option.
A) 40.5 B) 41.5 C) 42.5 D) 43.5 E) 44.5
Let the distance between City X and Y be D   As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00   So it takes him 3 hours to cover distance D.   Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.   Now see,   A takes 3 hrs takes to cover distance D   so in 1.5 hrs A will cover D / 2 distance   Now see another part -   "On its way, it meets B at 3 PM and reaches Y at 5 PM."   Given that - B leaves City Y at 2 PM   So distance covered by A in 1 hr (3 - 2) = D / 3   Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is   D / 2 [when they first overtake] - D / 3 [when they again overtake]   = D / 6   Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )   =1.5 + 2 + 1= 
<gadget id="calculator">1.5 + 2 + 1</gadget>
<output>4.5</output>
4.5   so to cover D / 6 distance B took 4.5 hr   to cover D distance B will take   (4.5 * 6)= 
<gadget id="calculator">  (4.5 * 6)</gadget>
<output>27</output>
27 hr.   Now "After how many hours will 41.5 reach to Y from the time A overtook him."   Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)= 13.5 + 1 + 27= 
<gadget id="calculator">13.5 + 1 + 27</gadget>
<output>41.5</output>
41.5   ANSWER:41.5
<result>B</result>
Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.