Games and Races

(11) In a 300 m race, A beats B by 15 meters. In a 400 m race, B beats C by 20 meters. How much start should A give to C in a 200 m race?

• (a) 20 meters
• (b) 30 meters
• (c) 40 meters
• (d) 10 meters

Answer

Correct Answer: (c) 40 meters
A : B = 300 : 285, \; B : C = 400 : 380. \; \text{Thus,} \; A : C = \frac{300}{285} \times \frac{400}{380} = \frac{40}{38} \times \frac{19}{19} = \frac{40}{38}. \; \text{For a 200 m race,} \; \frac{40}{38} \times 200 = 210.53 \; \text{meters (approximately).} \; \text{Therefore, A should give C 40 meters start.}

(12) In a 500 m race, X beats Y by 50 meters. In a 1000 m race, how much start should X give to Y for a fair competition?

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

Answer

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

(13) In a 600 m race, P can beat Q by 60 meters. In a 1200 m race, how much start should P give to Q for a fair competition?

• (a) 80 meters
• (b) 120 meters
• (c) 60 meters
• (d) 200 meters

Answer

Correct Answer: (b) 120 meters
P : Q = 600 : 540. \; \text{For a 1200 m race,} \; \frac{600}{540} \times 1200 = 1333.33 \; \text{meters (approximately).} \; \text{Therefore, P should give Q 120 meters start for a fair competition.}

(14) In a 800 m race, R can beat S by 40 meters. In a 1600 m race, how much start should R give to S for a fair competition?

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

Answer

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

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

• (a) 50 meters
• (b) 70 meters
• (c) 90 meters
• (d) 110 meters

Answer

Correct Answer: (b) 70 meters
M : N = 700 : 665. \; \text{For a 1400 m race,} \; \frac{700}{665} \times 1400 = 1479.70 \; \text{meters (approximately).} \; \text{Therefore, M should give N 70 meters start for a fair competition.}