Races and games
- 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
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B covers 200 m while A 190 m
B covers 180 m while A 190 / 200 * 180 = 171 mCorrect Option: B
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.
- 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 ?
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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 pointsCorrect Option: A
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.
- 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:
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∴ A runs 100 m while B runs 95 m
∴ A runs 400 m while B runs 95 x 400 / 100 = 380 mCorrect Option: B
∴ 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
- 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?
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Time taken by A in one round = 3000 / 200 = 15 min.
Time taken by B in one round = 3000 / 150 = 20 min
2nd Method to solve this
Let us assume after T minutes both will meet first time together at starting points.
According to question,
200T - 150T = 3000 As we know (3 KM = 3000 meters)Correct Option: C
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
- Three men Ram, Karan and Mohan run around an oval garden from a fixed post at the rates of 5, 51⁄7, 51⁄3 per hour. They come back to the fixed post in 33⁄4 hours. Find the greatest length, the race course can have.
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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 / 7Correct Option: B
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
