## Races and games

#### Races and games

1. In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?
1. 12
2. 10
3. 8
4. 6

1. In a Game of 80 points,
A scores 80 points , B scores 75 points and C scores 65 points.
∵ B scores 75 points while A 80
∴ B scores 60 points while A = 80 x 60 / 75 = 64

##### Correct Option: C

∵ B scores 75 points while A 80
∴ B scores 60 points while A = 80 x 60 / 75 = 64
Again, A scores 80 points while C = 65
∴ A scores 64 points while C = 65 x 64 / 80 = 52 points
Hence, in a game of 60, B can give C (60 – 52) = 8 points

1. Two men A and B run a 500 m race, A having 140 m start, their speeds are as 3 : 4. Then, A wins by :
1. 10 m
2. 20 m
3. 40 m
4. 60 m

1. Here, A will have to cover a distance of (500 – 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.

##### Correct Option: B

Here, A will have to cover a distance of (500 – 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.
∴ A covers 360 m while B covers 4 x 360/ 3 = 480 m
Hence, B will be (500 – 480) = 20 m behind the winning post.
∴ A wins by 20 m.

1. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?
1. 364 m
2. 254 m
3. 324 m
4. 354 m

1. Clearly, if A runs 600 meters, B runs = 540 m.

##### Correct Option: C

Clearly, if A runs 600 meters, B runs = 540 m.
∴ If A runs 400 m, B runs = 540 x 400 / 600 = 540 x 4 / 6 = 90 x 4 = 360 m
Again, when B runs 500 m, C runs = 450 m
∴ When B runs 360 m, C runs = 450 x 360 / 500 = 45 x 36 / 5 = 9 x 36 = 324 m.
∴ A beats C by 400 - 324 = 76 m.

1. In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meter will A beat C in a race of 400 m?
1. 78 m
2. 56 m
3. 76 m
4. 86 m

1. If A runs 600 m, B runs 600 - 60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500 - 50 = 450 m.

##### Correct Option: C

If A runs 600 m, B runs 600 - 60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500 - 50 = 450 m.
∴ When B runs 360 m, C runs = 450 * 360 / 500 = 324 m
∴ A beats C by 400 - 324 = 76 m.

1. In a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?
1. 20
2. 30
3. 40
4. 50

1. When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90 - 18) = 72 points.
∴ When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.

##### Correct Option: A

When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90 - 18) = 72 points.
∴ When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.
A : B : C = 75 : 50 : 60
C : B = 60 / 50 = 120 / 100
So, in a game of 120, C can give B
(120 - 100) = 20 points.