Games and Races

(31) In a 200 m race, A beats B by 20 meters. In a 300 m race, how much start should B give to A for a fair competition?

• (a) 10 meters
• (b) 15 meters
• (c) 30 meters
• (d) 25 meters

Answer

Correct Answer: (c) 30 meters
A : B = 200 : 180. \; \text{For a 300 m race,} \; \frac{200}{180} \times 300 = 333.33 \; \text{meters (approximately).} \; \text{Therefore, B should give A 30 meters start for a fair competition.}

(32) In a 400 m race, X beats Y by 40 meters. In a 600 m race, how much start should Y give to X for a fair competition?

• (a) 50 meters
• (b) 60 meters
• (c) 75 meters
• (d) 80 meters

Answer

Correct Answer: (c) 75 meters
X : Y = 400 : 360. \; \text{For a 600 m race,} \; \frac{400}{360} \times 600 = 666.67 \; \text{meters (approximately).} \; \text{Therefore, Y should give X 75 meters start for a fair competition.}

(33) In a 500 m race, P can beat Q by 25 meters. In an 800 m race, how much start should P give to Q for a fair competition?

• (a) 80 meters
• (b) 100 meters
• (c) 125 meters
• (d) 150 meters

Answer

Correct Answer: (c) 125 meters
P : Q = 500 : 475. \; \text{For an 800 m race,} \; \frac{500}{475} \times 800 = 842.11 \; \text{meters (approximately).} \; \text{Therefore, P should give Q 125 meters start for a fair competition.}

(34) In a 600 m race, R beats S by 30 meters. In an 800 m race, how much start should S give to R for a fair competition?

• (a) 32 meters
• (b) 36 meters
• (c) 40 meters
• (d) 45 meters

Answer

Correct Answer: (c) 40 meters
R : S = 600 : 570. \; \text{For an 800 m race,} \; \frac{600}{570} \times 800 = 842.11 \; \text{meters (approximately).} \; \text{Therefore, S should give R 40 meters start for a fair competition.}

(35) In an 800 m race, M beats N by 40 meters. In a 1600 m race, how much start should N give to M for a fair competition?

• (a) 120 meters
• (b) 160 meters
• (c) 320 meters
• (d) 240 meters

Answer

Correct Answer: (c) 320 meters
M : N = 800 : 760. \; \text{For a 1600 m race,} \; \frac{800}{760} \times 1600 = 1684.21 \; \text{meters (approximately).} \; \text{Therefore, N should give M 320 meters start for a fair competition.}