## Races and games

#### Races and games

1. In 1 km race, A beats B by 18 m or 9 s. Find the A' s time over the course.
1. 391 s
2. 591 s
3. 491 s
4. 500 s

1. Clearly, B covers 18 m in 9 s.
∴ B's time over the course = 9/18 x 1000 = 500 s

##### Correct Option: C

Clearly, B covers 18 m in 9 s.
∴ B's time over the course = 9/18 x 1000 = 500 s
∴ A' s time over the course = (500 - 9) = 491 s

1. In a 1000 m race, X beats Y by 140 m or 14 s. What will be the X's time over the course?
1. 86 s
2. 90 s
3. 95 s
4. 76 s

1. Clearly, Y covers 140 m in 14 s
∴ Y' s time over the course = (14/140) x 1000 = 100 s

##### Correct Option: A

Clearly, Y covers 140 m in 14 s
∴ Y' s time over the course = (14/140) x 1000 = 100 s
∴ X' s time over the course = 100 - 14 = 86 s

1. In a 400 m race, A runs at a speed of 16 m/s. If A gives B a start of 16 m and still beats him by 40 s, What will be the speed of B?
1. 6 m/s
2. 8 m/s
3. 15 m/s
4. 5.9 m/s

1. Time taken by A to cover 400 m = Distance/ Speed
= 400/16 s = 25 s
∴ B covers (400 -16) = 384 m in(25 + 40) = 65 s

##### Correct Option: D

Time taken by A to cover 400 m = Distance/ Speed
= 400/16 s = 25 s
∴ B covers (400 -16) = 384 m in(25 + 40) = 65 s
∴ B's speed = 384/65 =5.9 m/s

1. A can run 45 m while B runs 50 m. In a km race B beats A by how many metres ?
1. 150 m
2. 200 m
3. 100 m
4. 125 m

1. When B runs 50 m, then A runs 45 m.
When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m

##### Correct Option: C

When B runs 50 m, then A runs 45 m.
When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m
∴ B beats A by 100 m.

1. A can run 200 m in 35 seconds and B in 38 seconds. By what distance A beats B?
1. 15 m
2. 1523 m
3. 151519 m
4. 15419 m

1. The distance covered by B in 35 seconds = 200 x 35 / 38 = 3500 / 19 m

##### Correct Option: C

The distance covered by B in 35 seconds = 200 x 35 / 38 = 3500 / 19 m
Now, 200 – 3500 / 19 = 300 / 19 = 151519 m Hence, A can beat B by 151519 m.