Games and Races

(21) In a 150 m race, A beats B by 15 meters. In a 300 m race, how much start should B give to A for a fair competition?

• (a) 25 meters
• (b) 30 meters
• (c) 20 meters
• (d) 35 meters

Answer

Correct Answer: (c) 20 meters
A : B = 150 : 135. \; \text{For a 300 m race,} \; \frac{150}{135} \times 300 = 333.33 \; \text{meters (approximately).} \; \text{Therefore, B should give A 20 meters start for a fair competition.}

(22) 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) 60 meters
• (b) 30 meters
• (c) 45 meters
• (d) 50 meters

Answer

Correct Answer: (c) 45 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 45 meters start for a fair competition.}

(23) 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) 50 meters
• (b) 75 meters
• (c) 125 meters
• (d) 100 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.}

(24) In a 600 m race, R beats S by 24 meters. In an 800 m race, how much start should S give to R for a fair competition?

• (a) 32 meters
• (b) 48 meters
• (c) 24 meters
• (d) 64 meters

Answer

Correct Answer: (a) 32 meters
R : S = 600 : 576. \; \text{For an 800 m race,} \; \frac{600}{576} \times 800 = 833.33 \; \text{meters (approximately).} \; \text{Therefore, S should give R 32 meters start for a fair competition.}

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

• (a) 80 meters
• (b) 120 meters
• (c) 160 meters
• (d) 320 meters

Answer

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