Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?
Choose one.
A) 300 kms from A
B) 280 kms from A
C) 305 kms from A
D) 295 kms from A
E) 265 kms from A
DETAILED SOLUTION   Bus A   Travels 200km @ 40kmph   the next 200km @ 50kmph and   the final 200km @ 60kmph   So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins   Bus B   Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip.   So, Bus B will travel   160 kms in the first 4 hours   200 kms in the next 4 hours   and 240 in the final 4 hours   So, both buses cross each other when they are in their middle legs.   After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50).   The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50= 
<gadget id="calculator">50 + 50</gadget>
<output>100</output>
100 kmph.   Time taken= 190/100= 
<gadget id="calculator">190/100</gadget>
<output>19/10 = around 1.9</output>
1.9 hours.= 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95= 
<gadget id="calculator">210 + 95</gadget>
<output>305</output>
305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A.   CORRECT ANSWER 295 kms from A
<result>D</result>
Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?