## Races and games

#### Races and games

1. In a Km race A beats B by 25 m or 5 sec. Then find out the time taken by A to complete the race.
1. 3 minutes 15 seconds
2. 4 minutes 20 seconds
3. 2 minutes 30 seconds
4. 5 minutes 10 seconds

1. B runs 25 m in 5 seconds.
∴ B’s time to cover 1 Km = 5 x 100 / 25 = 200 sec

##### Correct Option: A

B runs 25 m in 5 seconds.
∴ B’s time to cover 1 Km = 5 x 100 / 25 = 200 sec
A’s time to cover one Km = 200 - 5 = 195 seconds
= 3 minutes 15 seconds.

1. In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
1. 100
2. 200
3. 300
4. 400

1. Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.

##### Correct Option: A

Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.
When B scores (P - 20) points,
C scores [( P - 15 ) / P * P (P - 20)] points
∴ (P - 15)( P - 20) / P = P - 20 or, P = 100
Hence, 100 points make the game.

1. A runner runs 114 laps of a 5 lap race. What fractional part of the race remains to be run?
1. 154
2. 45
3. 56
4. 23

1. race remains to be run = 5 - 54

##### Correct Option: A

race remains to be run = 5 - 54 = 154 .

1. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet next at the starting point again?

1. 46 minutes 12 seconds
2. 45 minutes
3. 42 minutes 36 seconds
4. 26 minutes 18 seconds

1. L.C.M. of 252, 308 and 198 = 2772 seconds

##### Correct Option: A

L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
.

1. Raju runs 1250 meter on Monday and Friday. Another days he runs 1500 meter except for Sunday (He does not run on Sunday). How many kilometer will he run in 3 weeks (first day starting from Monday)?
1. 12.5 Km
2. 20.5 Km
3. 8.5 Km
4. 25.5 Km
5. None of these

1. Raju runs on Monday and Friday = 1250 × 2 = 2500 m
On Tuesday, Wednesday, Thursday and Saturday,
Raju runs 1500 × 4 = 6000 m

##### Correct Option: D

Raju runs on Monday and Friday = 1250 × 2 = 2500 m
On Tuesday, Wednesday, Thursday and Saturday,
Raju runs 1500 × 4 = 6000 m
In 1 week Raju runs 6000 + 2500 = 8500 m
In 3 weeks Raju runs 3 × 8500 = 25500 m = 25.5 K