Games and Races

(6) In a 200 m race, X can give Y a start of 20 meters and still win by 10 meters. How long does it take X to run the race?

• (a) 24 seconds
• (b) 20 seconds
• (c) 28 seconds
• (d) 16 seconds

Answer

Correct Answer: (b) 20 seconds
X : Y = 200 : 180. \; \text{To win by 10 meters, X needs to run 200 meters.} \; \text{Therefore, it takes X 20 seconds to run the race.}

(7) In a 300 m race, M can beat N by 30 meters. In a 400 m race, N can beat O by 20 meters. How much start should M give to O in a 200 m race?

• (a) 16 meters
• (b) 20 meters
• (c) 12 meters
• (d) 24 meters

Answer

Correct Answer: (c) 12 meters
M : N = 300 : 270, \; N : O = 400 : 380. \; \text{Thus,} \; M : O = \frac{300}{270} \times \frac{400}{380} = \frac{40}{36} \times \frac{19}{19} = \frac{40}{36}. \; \text{For a 200 m race,} \; \frac{40}{36} \times 200 = 220 \; \text{meters.} \; \text{Therefore, M should give O 12 meters start.}

(8) In a 500 m race, R beats S by 50 meters. If they run a 1000 m race, how much start should R give to S for a fair competition?

• (a) 100 meters
• (b) 200 meters
• (c) 50 meters
• (d) 150 meters

Answer

Correct Answer: (a) 100 meters
R : S = 500 : 450. \; \text{For a 1000 m race,} \; \frac{500}{450} \times 1000 = 1111.11 \; \text{meters (approximately).} \; \text{Therefore, R should give S 100 meters start for a fair competition.}

(9) In a 600 m race, T can beat U by 60 meters. If T and U run a 400 m race, how much start should T give to U for a fair competition?

• (a) 40 meters
• (b) 30 meters
• (c) 50 meters
• (d) 20 meters

Answer

Correct Answer: (b) 30 meters
T : U = 600 : 540. \; \text{For a 400 m race,} \; \frac{600}{540} \times 400 = 444.44 \; \text{meters (approximately).} \; \text{Therefore, T should give U 30 meters start for a fair competition.}

(10) In a 800 m race, V beats W by 40 meters. In a 1600 m race, how much start should V give to W for a fair competition?

• (a) 80 meters
• (b) 120 meters
• (c) 60 meters
• (d) 240 meters

Answer

Correct Answer: (d) 240 meters
V : W = 800 : 760. \; \text{For a 1600 m race,} \; \frac{800}{760} \times 1600 = 1684.21 \; \text{meters (approximately).} \; \text{Therefore, V should give W 240 meters start for a fair competition.}