Games and Races

(16) In a 200 m race, A beats B by 10 meters. If they run a 400 m race, how much start should B give to A for a fair competition?

• (a) 20 meters
• (b) 15 meters
• (c) 25 meters
• (d) 30 meters

Answer

Correct Answer: (b) 15 meters
A : B = 200 : 190. \; \text{For a 400 m race,} \; \frac{200}{190} \times 400 = 421.05 \; \text{meters (approximately).} \; \text{Therefore, B should give A 15 meters start for a fair competition.}

(17) In a 300 m race, X beats Y by 15 meters. In a 900 m race, how much start should Y give to X for a fair competition?

• (a) 30 meters
• (b) 45 meters
• (c) 60 meters
• (d) 75 meters

Answer

Correct Answer: (b) 45 meters
X : Y = 300 : 285. \; \text{For a 900 m race,} \; \frac{300}{285} \times 900 = 947.37 \; \text{meters (approximately).} \; \text{Therefore, Y should give X 45 meters start for a fair competition.}

(18) In a 500 m race, P can beat Q by 25 meters. In a 1000 m race, how much start should Q give to P for a fair competition?

• (a) 50 meters
• (b) 75 meters
• (c) 100 meters
• (d) 125 meters

Answer

Correct Answer: (c) 100 meters
P : Q = 500 : 475. \; \text{For a 1000 m race,} \; \frac{500}{475} \times 1000 = 1052.63 \; \text{meters (approximately).} \; \text{Therefore, Q should give P 100 meters start for a fair competition.}

(19) In a 600 m race, R beats S by 30 meters. If they run a 300 m race, how much start should S give to R for a fair competition?

• (a) 60 meters
• (b) 90 meters
• (c) 30 meters
• (d) 120 meters

Answer

Correct Answer: (a) 60 meters
R : S = 600 : 570. \; \text{For a 300 m race,} \; \frac{600}{570} \times 300 = 315.79 \; \text{meters (approximately).} \; \text{Therefore, S should give R 60 meters start for a fair competition.}

(20) In a 700 m race, M beats N by 42 meters. In an 800 m race, how much start should N give to M for a fair competition?

• (a) 56 meters
• (b) 28 meters
• (c) 48 meters
• (d) 64 meters

Answer

Correct Answer: (c) 48 meters
M : N = 700 : 658. \; \text{For an 800 m race,} \; \frac{700}{658} \times 800 = 851.94 \; \text{meters (approximately).} \; \text{Therefore, N should give M 48 meters start for a fair competition.}