Race

In a kilometer race, A beats B by 10 meters. In a two-kilometer race, A beats B by how many meters?

• To understand this, let's break it down. In a 1-kilometer race, A beats B by 10 meters. This means that for every 1 kilometer, A gains a lead of 10 meters over B.
• Now, in a 2-kilometer race, A will maintain the same pace. So, for the first kilometer, A gains 10 meters on B, and for the second kilometer, A again gains 10 meters. Therefore, in total, A beats B by 20 meters in a 2-kilometer race.
• This logic extends to longer races as well. For every additional kilometer, A gains another 10 meters on B. Hence, in a 3-kilometer race, A would beat B by 30 meters.
• So, the answer is that in a two-kilometer race, A beats B by 20 meters.

In a 1500 meter race, Anil beats Bakul by 150 meters, and in the same race, Bakul beats Charles by 75 meters. By what distance does Anil beat Charles?

• This problem might seem straightforward, but it requires careful calculation. Anil beats Bakul by 150 meters, and Bakul beats Charles by 75 meters. Therefore, adding 150 + 75 won't give the correct answer. Instead, we need to create separate 1500 meter races for Bakul and Charles and analyze the ratios.

                   Anil    Bakul   Charles
                   1500    1350    
                            1500   1425
                

• We find the ratio by making Bakul's distance common. Anil beats Bakul by 150 meters, so Bakul runs 1350 meters when Anil completes 1500 meters. Bakul beats Charles by 75 meters, so Charles runs 1425 meters when Bakul completes 1500 meters.

                   Anil    Bakul   Charles
                   1500    1350    1350
                   1500    1500    1425
                

• Now, we calculate the ratio and find the equivalent distance for Anil and Charles:
  • 1500 * 1500 : 1350 * 1425
  • 200 : 171
  • Now, if 200 units represent 1500 meters,
  • 1 unit = 1500 / 200 = 7.5 meters
  • Anil is ahead of Charles by 200 - 171 = 29 units
  • In meters, this distance is 29 * 7.5 = 217.5 meters
• Therefore, Anil beats Charles by 217.5 meters.

In a 100-meter race, A beats B by 20 meters, and B beats C by 20 meters. By how much distance does A beat C?

 A    B   C
100  80   
     100  80 

• Let's analyze the race distances to understand the problem. A beats B by 20 meters, meaning when A runs 100 meters, B runs 80 meters. Similarly, B beats C by 20 meters, so when B runs 100 meters, C runs 80 meters.

 A    B   C
100  80   80
100  100  80 

• We now calculate the ratio and find the equivalent distance for A and C:
  • 100 * 100 : 80 * 80
  • 25 : 16
  • Now, if 25 units represent 100 meters,
  • 1 unit = 100 / 25 = 4 meters
  • A beats C by 25 - 16 = 9 units
  • In meters, this distance is 9 * 4 = 36 meters
• Therefore, A beats C by 36 meters.

In a race of 800 meters, A beats B by 40 meters. In a 500-meter race, B beats C by 5 meters. By how many meters will A beat C in a race of 200 meters?

• Since the races are of different lengths, we need to adjust the distances proportionally.

 A    B    C
800  760   
     500  495 

 A    B    C
800  760  760 
500  500  495 

• We now calculate the ratio and find the equivalent distance for A and C:
  • A : C
  • 800 * 500 : 760 * 495
  • 400000 : 376200
  • Simplify the ratio:
  • 400000 / 200 = 2000
  • 376200 / 200 = 1881
  • The simplified ratio is 2000 : 1881
  • Now, we need to scale this ratio down to a 200-meter race:
  • For a 200-meter race, we use the ratio 2000 : 1881
  • 2000 units represent 200 meters
  • 1 unit = 200 / 2000 = 0.1 meters
  • A beats C by 2000 - 1881 = 119 units
  • In meters, this distance is 119 * 0.1 = 11.9 meters
• Therefore, in a 200-meter race, A will beat C by 11.9 meters.

In a race of 600 meters, Jay beats Veeru by 60 meters, and in a race of 500 meters, Veeru beats Robert by 25 meters. By how many meters will Jay beat Robert in a 400-meter race?

Jay   Veeru   Robert
600   540   
      500    475 
                

• We need to determine the ratio to find out by how many meters Jay will beat Robert in a 400-meter race.

Jay   Veeru   Robert
600    540     540
500    500     475 
                

• To find Jay's lead over Robert:
  • Jay : Robert
  • 600 * 500 : 540 * 475
  • 300000 : 256500
  • Simplify the ratio:
  • 300000 / 1500 = 200
  • 256500 / 1500 = 171
  • The simplified ratio is 200 : 171
  • If 200 units represent 400 meters,
  • 1 unit = 400 / 200 = 2 meters
  • Jay is ahead of Robert by 200 - 171 = 29 units
  • In meters, this distance is 29 * 2 = 58 meters
• Therefore, in a 400-meter race, Jay will beat Robert by 58 meters.