Races and Games Questions

Time gap to infer the slower speed: In a 100 m race, Kamal defeats Bimal by 5 s. If Kamal’s speed is 18 km/h, what is Bimal’s speed (km/h)?

Repeat of start + time-gap computation: In a 100 m race, A runs at 5 km/h, gives B a start of 8 m, and still beats B by 8 s. Find B’s speed.

Transferring race results between contestants: In a 1 km race, A beats B by 100 m and C by 200 m. By how many metres can B beat C in a 1350 m race?

Beating distance from 1 km times: A runs 1 km in 3 min 10 s (190 s), and B runs 1 km in 3 min 20 s (200 s). Starting together for 1 km, by what distance does A beat B?

Billiards handicap translation: In a 120-point game, A can give B 20 points and C 30 points. In a 90-point game, how many points can B give C?

Overtaking time with staggered starts: Arun starts from P at 6:00 am at 8 km/h. Bhaskar starts from P at 7:30 am at 12 km/h, both running in the same direction. At what time does Bhaskar overtake Arun?

Catch-up times from staggered starts and different speeds: A, B, C walk 1 km in 5 min, 8 min, and 10 min, respectively. C starts at t = 0, B starts 1 min later, and A starts 2 min later than C. After A starts, when does A catch B and C (times in minutes)?

A 10 km race is held on an 800 m circular track. Two runners P and Q compete, and their speeds are in the ratio 5 : 4. When the winner completes the full 10 km, how many complete times does the winner overtake (lap) the other on the track?

A runs at 1 2/3 (that is, 5/3) times the speed of B. If A gives B a start of 40 m and they finish together, how far from A’s starting line should the winning post be placed?

In a 20 m race, A runs at 2 m/s. A gives B a 10 m head-start and still beats B by 5 seconds. What is B’s speed (in m/s)?

Shantanu cycles along the boundary of a square field ABCD starting at corner A. After 1/2 hour he reaches corner C (the corner diagonally opposite A) by following the boundary. If his cycling speed is 16 km/h, what is the area of the square field?

In an 800 m race, A can beat B by 40 m (so B covers 760 m when A finishes 800 m). In a 500 m race, B can beat C by 5 m (so C covers 495 m when B finishes 500 m). By how much does A beat C in a 200 m race?

Three runners Ram, Karan, and Mohan start from a fixed post around an oval at speeds 5 km/h, 5 1/7 km/h, and 5 1/3 km/h respectively. They all return to the fixed post exactly in 3 3/4 hours. What is the greatest possible track length (in km) consistent with this?

A and B start together and run in the same direction on a 3 km circular track. Their speeds are 200 m/min and 150 m/min respectively. After how long will they both be together again at the starting point?

A can beat B by 5 m in a 100 m race (so B covers 95 m when A covers 100 m). B can beat C by 15 m in a 200 m race (so C covers 185 m when B covers 200 m). By how many meters will A beat C in a 400 m race?

In billiards, A can give B 6 points in a game to 50, and A can give C 13 points in a game to 65. In a game to 55, how many points can B give C (so that the game is fair)?

In a 200 m race, B can give A a start of 10 m (so A runs 190 m when B runs 200 m). In the same 200 m race, C can give B a start of 20 m (so B runs 180 m when C runs 200 m). How much start can C give A in the same race?

A runs 500 m in 30 s; B runs 500 m in 35 s. In a 1 km race, how much head-start (in meters) should A give B so that they finish in a dead heat?

A’s speed is 1 3/8 times B’s speed (that is, 11/8 of B). In a race, A gives B a start of 300 m and they finish together. What should be the total race length (distance A runs) so both reach the winning post simultaneously?

In a 1 km race, A beats B by 80 m (i.e., B covers 920 m when A covers 1,000 m), and B beats C by 60 m (i.e., C covers 940 m when B covers 1,000 m). By how many meters does A beat C in the same 1 km race?