Bunuel wrote:
Two buses, A and B, are going from city P to city Q and back without a break. Bus A starts from city P and is moving at constant speed of 50km/h, bus B also starts from city P and is moving at constant speed of 20km/h. If the distance between the cities is 1,400 km, how far will bus A be from city Q when the buses meet for the 22nd time?
A. 400 km
B. 600 km
C. 1,000 km
D. 1,200 km
E. 1,400 km
Are You Up For the Challenge: 700 Level QuestionsThe two buses start together from P, and their speed is in ratio A:B = 5:2, so the distance covered will be in ratio 2:5.
Therefore, when A makes 5 trips one way, B makes 2 trips one way, and at the end of this A is at Q and B is at P.
Another 5 trips by A, and both A and B will be together at P in original position.
In these 10 rounds, the distance covered by both combined is (10+4)*1400 = 14*1400.
When they meet together at original point, we can say that average distance covered per meet is 1400*2=2800, so they meet 14*1400/2800=7 times..
Now extrapolating this further, when they meet 21st time, that is 7*3, they both will be at P.
So A will meet B after turning from Q, and combined distance will be 2800, so time taken = 2800/(20+50)=40 hr.
In 40 hr A will travel 40*50=2000=1400+600.
So A touches Q after travelling 1400 and is 600 km from Q when it meets B for 22nd time.
B