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Two motorcyclists, Ajay and Vijay, start simultaneously from a point S on an oval track and drive around the track in the same direction, with speeds of 29 km/hr and 19 km/hr respectively. Every time Ajay overtakes Vijay (anywhere on the track), both of them decrease their respective speeds by 1 km/hr. If the length of the track is 1 km, how many times do they meet at the starting point before Vijay comes to rest?
A. 2
B. 3
C. 5
D. 6
E. None of these
Are You Up For the Challenge: 700 Level Questions
A. 2
B. 3
C. 5
D. 6
E. None of these
Are You Up For the Challenge: 700 Level Questions
19 Aug 2022, 23:57
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Two motorcyclists, Ajay and Vijay, start simultaneously from a point S on an oval track and drive around the track in the same direction, with speeds of 29 km/hr and 19 km/hr respectively. Every time Ajay overtakes Vijay (anywhere on the track), both of them decrease their respective speeds by 1 km/hr. If the length of the track is 1 km, how many times do they meet at the starting point before Vijay comes to rest?
A. 2
B. 3
C. 5
D. 6
E. None of these
A. 2
B. 3
C. 5
D. 6
E. None of these
You will not see such a question on GMAT, but it is always good to exercise your brain.
Whenever A and V meet, A has covered 1 km over V as the track is of one km.
B
Also, A would cover (29-19) or 10km extra in one hour. Thus, 1 km in \(\frac{1}{10}\) hr. Even when both drop their speeds by 1kmph, the time they meet will be 1/10 hr as 28-18 or 27-17 will be 10.
Now, B would travel 19*1/10 and then 18*1/10 and so on.
B would be at Start point whenever the combined distance 19*1/10 + 18*1/10 + 17*1/10 + ….. is an integer.
OR
1.9+1.8+1.7+….. is an integer.
Now, 1.9+1.8+1.7+1.6 is 6, so they will meet at the start point after 4*1/10 hr or 24 minutes.
Next, 1.5+1.4+1.3+1.2+1.1+1.0+0.9+0.8+0.7+0.6+0.5 will give 10
The time speed is 4 and below, the distance travelled is 0.4+0.3+0.2+0.1 or 1.
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