Games and Races

(26) In a 200 m race, A beats B by 10 meters. In a 300 m race, how much start should B give to A for a fair competition?

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

Answer

Correct Answer: (c) 15 meters
A : B = 200 : 190. \; \text{For a 300 m race,} \; \frac{200}{190} \times 300 = 315.79 \; \text{meters (approximately).} \; \text{Therefore, B should give A 15 meters start for a fair competition.}

(27) In a 400 m race, X beats Y by 40 meters. In a 500 m race, how much start should Y give to X for a fair competition?

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

Answer

Correct Answer: (c) 50 meters
X : Y = 400 : 360. \; \text{For a 500 m race,} \; \frac{400}{360} \times 500 = 555.56 \; \text{meters (approximately).} \; \text{Therefore, Y should give X 50 meters start for a fair competition.}

(28) In a 600 m race, P can beat Q by 30 meters. In an 800 m race, how much start should P give to Q for a fair competition?

• (a) 100 meters
• (b) 40 meters
• (c) 80 meters
• (d) 60 meters

Answer

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

(29) In a 500 m race, R beats S by 20 meters. In a 1000 m race, how much start should S give to R for a fair competition?

• (a) 40 meters
• (b) 80 meters
• (c) 60 meters
• (d) 100 meters

Answer

Correct Answer: (a) 40 meters
R : S = 500 : 480. \; \text{For a 1000 m race,} \; \frac{500}{480} \times 1000 = 1041.67 \; \text{meters (approximately).} \; \text{Therefore, S should give R 40 meters start for a fair competition.}

(30) In a 700 m race, M beats N by 35 meters. In a 1400 m race, how much start should N give to M for a fair competition?

• (a) 50 meters
• (b) 70 meters
• (c) 90 meters
• (d) 105 meters

Answer

Correct Answer: (d) 105 meters
M : N = 700 : 665. \; \text{For a 1400 m race,} \; \frac{700}{665} \times 1400 = 1479.70 \; \text{meters (approximately).} \; \text{Therefore, N should give M 105 meters start for a fair competition.}