Answer: 150m

Explanation:
Since X runs 1 ½ times, i.e. 3/2 times as fast as Y, the time Y runs 2 m X runs 3m, i.e X gains 1 m for every 3 m he runs. Since he gave lead of 50 m, they will meet at ( 3 × 50)m i.e. 150m

Answer: A and 16.67 sec

Explanation:
D = 10 × 1000 = 1000m
SA = 60 × 5/18 = 150 / 9 m/s
SB = 54 × 5/18 = 15 m/s
TA = 1000/150 × 9 = 600 sec
Total time for A = 600 + 50 = 650 sec
TB = 1000/15 = 666.66sec
A won by 666.66 – 650 = 16.66 sec

Answer: 9:7

Explanation:
When they meet, the faster man has completed 4 ½ rounds, whereas
=>The slower man has completed 3 ½ rounds. Since these distances have been covered in the same time, the ratio of distances = the ratio of speeds = 4.5 :3.5 = 9:7

Answer: 6 sec

Explanation:
suppose the two bodies need X and (X + 2) seconds to complete one
=> Round of the track. The two bodies will meet at a time equal to the LCM of the times they require to complete one round each. It has been given that LCM [X, (X+2)] = 12 seconds.
It can therefore be estimated that X = 4 seconds and (X + 2) = 6 seconds.

Answer: 10 m/s

Explanation:
A beats by 7 * 1/7 seconds. A gives B a start of 5 seconds and
=> Still beats him by 15 m.
=> There, B takes 7 * 1/7 – 5 = 2 * 1/7 seconds to run 15 m
=> Therefore, B’s speed is 15(15/7) = 7 m/s. to complete a 400 m race,
=> B takes 400/7 seconds and A takes 400/7 – 50/7 = 50 seconds.
Therefore, A’s speed is 400/50 = 8 m/s

Answer: 13 kmph

Explanation:
to win the race Arjun will have to cover the distance of 200m
=> While Karna will have to cover the distance of only 195m as Arjun gives Karna 5m.
=> Speed of Arjun is 15kmph so time taken by arjun will be (200 x 18)/(15 x 5) i.e. 48 sec. arjun beats Karna by 6 sec. so time taken by karna to cover the distance of 195m will be (48 + 6) i.e. 54 sec
Hence the speed of Karna = (195/54)(18/5) = 13kmph

Answer: 1200m

Explanation:
Let S be the starting point of the race. A and B run at speeds of
=> Sa and Sb. A is the point where A and B meet for the first time and B is the point where A and B meet the second time.
=> When they meet, A and B cover different distances in the same time. So, the ratio of the distances covered is the same as the ratio of their speed.
=> So, Sa/Sb = 450 / (300 + X) = X/750. Solving this equation, we get X = 450 m
The length of the track is 450 + 450 + 300 = 1200 m

Answer: 5 hours 52 minutes 

Explanation:
A and B move at a relative speed of (160 – 120) = 40 m/minute
=> A and B come together in 1760/40 = 44 minutes
=> A and C move together at a relative speed of (160 – 105)
=> = 55 m/minutes
=> A and C come together in (1760/55) = 32 minutes
=> A, B and C come together in 352 minutes (LCM of 44 and 32)
A, B and C come together in 5 hours 52 minutes.

Answer: 20 m    

Explanation:
Distance covered by B in 9 secs = (100/45 * 9) = 20 m
Hence, A beats B by 20 m.

Answer: 33 sec   

Explanation:
B runs 35 m in 7 sec.
Hence, B covers 200 m in (7/35 * 200) = 40 sec
B’s time over the course = 40 sec
A’s time over the course = (40 – 7) = 33 sec