Races and Games problems
- 1. Shantanu started cycling along the boundaries of a square field ABCD from corner point A. After 1/2 h, he reached the corner point C, diagonally opposite to point A. If his speed was 16 km/h. Find the area of the field?
Options- A. 8 sq km
- B. 9 sq km
- C. 19 sq km
- D. None of the above Discuss
Correct Answer: None of the above
Explanation:
Distance = (AB + BC) = 2L = 16 x 1/2 = 8 km
? L = 8/2 = 4 km
? Area of the field = 4 x 4 = 16 sq km.
- 2. In a race of 800 meter, A can beat B by 40 meter. In a race of 500 meter, B can beat C by 5 meter. In a race of 200 meter, A will beat C by
Options- A. 12.7 m
- B. 11.9 m
- C. 1.27 m
- D. 1.19 m Discuss
Correct Answer: 11.9 m
Explanation:
In a 800 meter race, A covers 800 meter while B cover 760 meter.
? A covers 200 m while B will cover 760 x 200 / 800 = 190 m
Again, B covers 500 m while C 495 m
? B covers 190 m while C will cover = 495 x 190 / 500 = 188.10 m
Since, A covers 200 m while C 188.10 m
Hence, A will beat C by (200 ? 188.10) = 11.9 m
- 3. Three men Ram, Karan and Mohan run around an oval garden from a fixed post at the rates of 5, 5 1? 7, 5 1? 3 per hour. They come back to the fixed post in 3 3? 4 hours. Find the greatest length, the race course can have.
Options- A. 28 / 5 km
- B. 5 / 28 km
- C. 11 / 28 km
- D. 28 / 11 km Discuss
Correct Answer: 5 / 28 km
Explanation:
Total number of rounds made by Ram in 15 / 4 hrs = 5 × 15 / 4 = 75 / 4
? Total number of rounds made by Karan in 15 / 4 hrs = 36 / 7 * 15 / 4 = 135 / 7
Total number of rounds made by Mohan in 15 / 4 hrs = 16 / 3 * 15 / 4 = 20
H.C.F. of 75 / 4 , 135 / 7 and 2 = 5 / 28
- 4. A and B start from the same point and travel in the same direction round a circular track 3 km in circumference. If their speed be 200 and 150 metres a minute, when will they first together again at the starting point?
Options- A. 40 min
- B. 55 min
- C. 1 hour
- D. 45 min Discuss
Correct Answer: 1 hour
Explanation:
Time taken by A in one round = 3000 / 200 = 15 min.
Time taken by B in one round = 3000 / 150 = 20 min
L.C.M. of 15 min and 20 min = 60 min = 1 hr.
Hence, they will meet first together at the starting point after 1 hour.
2nd Method to solve this
Let us assume after T minutes both A and B will meet first time together at starting points.
According to question,
Distance covered by A in T minutes = 200 x T = 200T
Distance covered by B in T minutes = 150 x T = 150T
200T - 150T = 3000 As we know (3 KM = 3000 meters)
? 50T = 3000
? 5T = 300
? T = 300/5 = 60 Minutes.
As we know ( 60 minutes = 1 hours)
? T = 1 Hours
- 5. A can beat B by 5 meters in 100 m and B can beat C by 15 meters in 200 m race. A can beat C in 400 m race by:
Options- A. 50.5 m
- B. 48.5 m
- C. 45.5 m
- D. 42.5 m Discuss
Correct Answer: 48.5 m
Explanation:
? A runs 100 m while B runs 95 m
? A runs 400 m while B runs 95 x 400 / 100 = 380 m
Again, B runs 200 m while C runs 185 m
? B runs 380 m while C runs 185 x 200 / 380 = 3515 / 10 = 351.5 m
Hence, A runs 400 m while C runs 351.5 m
So, A can beat C by (400 ? 351.5) = 48.5 m
- 6. At a game of billiards A can give B 6 points in 50 and he can give C 13 points in 65, how many points can B give C in a game of 55?
Options- A. 7
- B. 8
- C. 5
- D. 10 Discuss
Correct Answer: 5
Explanation:
In a game of 50, If A scores 50 then B scores 44.
? A scores 65 while B 44 * 65 / 50 = 57.2 points
Now, B scores 57.2 points while C 52
? B scores 55 points while C = 52 * 55 / 57.2 = 50
Hence, in game of 55 points B can give C (55 ? 50) = 5 points
- 7. In a race of 200 metres, B can give a start of 10 metres to A and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is
Options- A. 30 m
- B. 29 m
- C. 27 m
- D. 25 m Discuss
Correct Answer: 29 m
Explanation:
B covers 200 m while A 190 m
B covers 180 m while A 190 x 180 / 200 = 171 m
Hence, C covers 200 m while A = 171 m
So, C can give to A (200 ? 171) = 29 m start.
- 8. A can run 500m in 30 seconds and B in 35 seconds. How many meter start can A give to B in a Km race so that the race may end in a dead-heat?
Options- A. 1395?7
- B. 1385?7
- C. 1426?7
- D. 1405?7 Discuss
Correct Answer: 1426?7
Explanation:
Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
? A can give B a start of (70 - 60) = 10 seconds.
In 35 sec B runs 500 m
? In 10 sec B runs = 500 × 10 / 35 = 1000 / 7 = 1426?7 meters
So, A can give B a start of 1426?7 meters in a Km race.
- 9. A's speed is 1 3? 8 times of B's. In a race A gives B a start of 300 m. How long should the race course be so that both reach the winning post simultaneously?
Options- A. 700 m
- B. 900 m
- C. 800 m
- D. 850 m Discuss
Correct Answer: 900 m
Explanation:
A's speed : B's speed = 11?2 : 1
= 3?2 : 1
= 3 : 2
It means that in a race of 3 m, A gains (3 - 2).
= 1 m over B. 1 m is gained by A in a race of 3 m.
? 300 m is gained by A in a race of = 3?1 × 300 = 900 m.
- 10. In a Km race A can beat B by 80 m and B can beat C by 60 m. In the same race, A can beat C by :
Options- A. 135.2 m
- B. 130.5 m
- C. 142 m
- D. 132.5 m Discuss
Correct Answer: 135.2 m
Explanation:
While A runs 1000 m, B runs 1000 - 80 = 920 m and
While B runs 1000 m, C runs 1000 - 60 =940 m.
? While B runs 920 m; C runs
940 / 1000 × 920 = 4324 / 5 m
? While B runs 920 m; C runs 940 × 920 / 1000 = 4324 / 5 m
? While A runs 1000 m, C runs 4324 / 5 m
? A can beat C by 1000 - 4324 / 5 = 676 / 5 = 1351?5 m.
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