Races and Games problems
- 1. In a 100 m race, Kamal defeats Bimal by 5 seconds. If the speed of Kamal is 18 Km/h, then the speed of Bimal is :
Options- A. 15.4 km/h
- B. 14.5 km/h
- C. 14.4 km/h
- D. 14 km/h Discuss
Correct Answer: 14.4 km/h
Explanation:
Time taken by Kamal to run 100 m = 100 / 18 x 5 / 18 = 20 s Therefore, time taken by Bimal to run 100 m = 20 + 5 = 25 s
Hence, Bimal's speed = 100 / 25 = 4 m/sec = 4 x 18 Km/h = 14.4 Km/h
- 2. In a 100 meter race, A runs at 5Km/h. A gives B a start of 8 meter and still beats him by 8 sec. Find out the speed of B.
Options- A. 6.14 Km/h
- B. 4.14 Km/h
- C. 3.14 Km/h
- D. 2.14 Km/h Discuss
Correct Answer: 4.14 Km/h
Explanation:
Time taken by A to cover 100 meters
= 100 ÷ (5 * 5 / 18) = 72 seconds.
? B covers (100 - 8) or, 92 meters in (72 + 8) or, 80 seconds.
? Speed of B = ( 92 / 80 ) * ( 16 / 5 ) = 4.14 Km/h.
- 3. In a Km race A beats B by 100 m and C by 200 m. By how many can B beat C in a race of 1350 m?
Options- A. 150 m
- B. 120 m
- C. 1200 m
- D. 210 m Discuss
Correct Answer: 150 m
Explanation:
While Arun's 1000 m, B runs 1000 - 100 = 900 m and C runs 1000 - 200 = 800 m.
? While B runs 900 m, C runs 800 m.
? While B runs 1350 m; C runs 800 / 900 × 1350 = 1200 m
? B can beat C by 1350 - 1200 = 150 m.
- 4. A can run a distance of 1 Km in 3 minutes 10 seconds and B can run the same distance in 3 minutes 20 seconds. If they start together, by what distance will A beat B?
Options- A. 50 m
- B. 30 m
- C. 36 m
- D. 60 m Discuss
Correct Answer: 50 m
Explanation:
According to question,
A can run a distance of 1 Km in 3 minutes 10 seconds and B can run the same distance in 3 minutes 20 seconds.
A beats B by 10 sec.
So distance covered by B in 10 sec. = (1000 *10 / 200) m = 50 m
? A beat B by 50 m.
- 5. In a game of billiards, A can give B 20 points in the game of 120 points and he can give C 30 points in the game of 120 points, How many points can B give C in a game of 90?
Options- A. 9 points
- B. 18 points
- C. 6 points
- D. 3 points Discuss
Correct Answer: 9 points
Explanation:
If A scores 120 points, then B scores 100 points and C scores 90 points.
When B scores 100 points, then C scores 90 points.
When B scores 90 points than C scores (90/100) x 90 points = 81 points
? B can give C, 9 points in a game of 90.
- 6. Arun and Bhaskar start from place P at 6:00 am and 7:30 am, respectively and run in the same direction. Arun and Bhaskar run at 8 km/h and 12 km/h. respectively. Bhaskar overtakes
Arun at?
Options- A. 10 : 30 am
- B. 9 : 00 am
- C. 11 : 30 am
- D. 1 : 00 am Discuss
Correct Answer: 10 : 30 am
Explanation:
Distance between Arun and Bhaskar at 7:30 am = 8 x 11/2 = 12 km
Time taken by Bhaskar in covering a distance of 12 km = 12/(12 - 8) = 3 h
? Required time = 10 : 30 am
- 7. A, B and C walk 1 km in 5 min, 8 min and 10 min, respectively, C starts walking from a points at a certain time, B starts from the same point 1 min later and A starts from the same
point 2 min later than C, Then, A meet B and C at times?
Options- A. 2 min, 3 min
- B. 4/3 min, 3 min
- C. 2 min, 5/3 min
- D. 1 min, 2 min Discuss
Correct Answer: 2 min, 5/3 min
Explanation:
A walks 1 km in 5 min.
Then, distance covered by A in 1 min = 1000/5 = 200 m
B walks 1 km in 8 min.
Then, distance covered by B in 1 min = 1000/8 = 125 m
C walks 1 km in 10 min.
Then, distance covered by C in 1 min = 1000/101 = 100 m
Let A meets B and C in x and y min, respectively.
Then, according to the question,
Distance covered by C in(x + 2) min = Distance covered by A in x min
? 100(x + 2) = 200 x
?100 x + 200 = 200 x
? 200 = 100 x
? x = 200/100 = 2 min
Now, for A and B
Distance covered by B in (y + 1) min = Distance covered by A in y min
? 125(y + 1) = 200y
? 125y + 125 = 200y
? 125 = 200y - 125y
? 125 = 75y
? y = 125/75 = 5/3 min.
- 8. A 10 km race is organised at 800 m circular race course. P and Q are the contestants of the race. If the ratio of the speed of P and Q is 5 : 4, how many times will the winner overtake the loser?
Options- A. 4 times
- B. 1 times
- C. 2 times
- D. 3 times Discuss
Correct Answer: 2 times
Explanation:
Speed of P : Speed of Q = 5 : 4
Time taken by P to cover 5 rounds = Time taken by Q to cover 4 rounds
Distance covered by P in 5 rounds = 5 x (800/1000) = 4 km
Distance covered by Q in 4 rounds = 4 x (800/1000) = 16/5 km
In 5 rounds, P will overtake Q every time. It means that after covering 4 km, P will overtake Q one time .
? After covering 10 km P will overtake Q, = (1/4) x 10 = 21/2 times
- 9. A runs 1 2/ 3 times as fast as B. If A gives B a start of 40 m, how far must the winning post be, so that A and B might reach it at the same time?
Options- A. 75 m
- B. 200 m
- C. 100 m
- D. 125 m Discuss
Correct Answer: 100 m
Explanation:
Ratio of the speeds of A and B = 5 : 3
Thus, in a race of 5m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
40 m will be gained by A in a race of (5/2) x 40 m = 100 m
? Winning post is 100 m away from the starting point.
- 10. In a 20 m race, A runs at a speed of 2 m/s. If A gives B a start of 10 m and still beats him by 5 s, what will be the speed of B?
Options- A. 117/21 m/s
- B. 317/21 m/s
- C. 21 m/s
- D. 2 m/s Discuss
Correct Answer: 117/21 m/s
Explanation:
Time taken by A to cover 200 m = 200/2 = 100 s
? B covers (200 - 10) = 190 m in (100 + 5) = 105 s
? B' s speed = 190/105 = 38/21 = 117/21 m/s
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