Bissoy.com
Doctors Medicines MCQs Q&A

A, B and C run a 1 km race. When A and B run, A wins by 300 m. When B and C run, C wins by 30 sec. When A and C runs, A wins by 50 sec. Difference between the time taken by B and A to run a race of 1000 m is –

A, B and C run a 1 km race. When A and B run, A wins by 300 m. When B and C run, C wins by 30 sec. When A and C runs, A wins by 50 sec. Difference between the time taken by B and A to run a race of 1000 m is – Correct Answer 50/7 seconds

Given:

Let the time taken by A to complete race be M sec.

Concept:

Find the speed of each person and then equate the speed of a person obtained from different cases.

Calculation:

Distance covered by B in M sec = 1000 – 300 = 700 m

⇒ Speed of A = 1000/M

⇒ Speed of B = 700/M

Time taken by C to cover 1000 m = M + 50

⇒ Speed of C = 1000/(M + 50) = 700/(M + 30)

On solving, M = 50/3 sec

Time taken by B to cover 1 km = 1000/700 × M = 500/21 sec

∴ Required difference = 500/21 – 50/3 = 50/7 sec

Related Questions

A and B run a kilometer and A wins by 25 sec. A and C run a kilometer and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometer is
A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometre is :
In 5 km race, if P gives Q 500 m start and P wins the race by 2.1 min. When Q wins the race by 1000 m if P gives 4.2 min start. Find the difference in the time taken by Q and P.
A beats B by 13 sec in a 250 m race, B beats C by 18 sec in a 400 m race, C beats D by 21 sec in 600 m race and D beats E by 36 sec in a 750 m race. What must be the speed of A in order to beat E by 200 m in a 1 km race? 
In a cricket match, a team made a score of 256 runs which included 16 fours and 7 sixes. From the remaining runs, 20% were scored by taking three runs in a ball, 44% by taking two runs in a ball and the remaining were taken as single runs per ball. If the team played a total of 300 balls, on what percentage of the balls no runs were scored?
John, Jack, Joseph and Jordan participated in a running race. Only the winner finished the race in 10 minutes. Which two pieces of information can tell you who the winner was? (i) John finished the race in 16 minutes . (ii) Joseph finished the race earlier than Jack by 2 minutes. (iii) Jack finished the race later than Jordan by 4 minutes. (iv) Jordan finished the race earlier than John by 6 minutes. (v) John finished the race later than Joseph by minutes.
Racing track is 250 m long. Rita and Disha run a race and Rita wins by 7 metres. Disha and Shweta run over the same course and Disha wins by 5 metres. Shweta and Mina run over it and Mina wins by 20 metres. If Rita and Mina run over it, then who would win and by how much?
The average of runs of a group of 20 players in match X is 40. If the score of another player A is added to the total score of the group, the average is reduced by 1 run. A scored 11 runs more in match Y than his score in the previous match. Now player B joins the group and the average is increased by two runs. What is the difference between the runs scored by player A in match X and the runs scored by player B in match Y?
In a 200 meters race, Rohan can give Rahul a 20 meters start and in a 36 km race Rahul can give Sanjay a 4 km start. If the speed of Rahul is 36 m/sec then what is the speed of Rohan in m/sec? A. 20 m/sec B. 40 m/sec C. 24 m/sec D. 50 m/sec
Rakesh and Abhinay are swimmers and they participated in a swimming race in which they had to travel between two ports A and B and returned back from B to A. Rakesh took 37.5 seconds to complete the race and Abhinay took 200/3 seconds to complete the race. If the speed of Abhinay is increased by 100% then find the approximate difference between the time taken by Rakesh and Abhinay to complete the race where the speed of stream is 5m/s and the distance between two ports is 250m.