In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra

Question

In a 200 meters race, A beats B by 20 meters, while in a 100 meters race, B beats C by 5 meters. A beats C in a kilometer race by

(A) 105 meters
(B) 145 meters
(C) 155 meters
(D) 205 meters
(E) 255 meters

GMATinsight · Accepted Answer

It can be done as Ratio question

--A-------B-------C
200-----180 
--------100------95

Combining the ratios we get

--A-------B --------C
1000-----900------ 855

i.e. when A runs 1000 meters then C runs 855 meters

1 km = 1000 meters

i.e. when A runs 1000 meters then C runs 855 meters

i.e. A beats C by = 1000-855 = 145 meters

Answer: Option B

LevanKhukhunashvili · Answer

200-meter race 
Let's assume that the speed of A=100 m/h
He will finish 200m distance in 2 hours

As B covers 20m less, then in 2 hours he covers 180m, so his speed is  \frac{180}{2} =90m/h

100-meter race 
With 90m/h speed, B covers 100m in  \frac{10}{9}  hours
So, C will cover 95m in  \frac{10}{9}  hours with the speed of 95* \frac{10}{9} =85.5m/h

1000m=1km race 
A covers 1000m with the speed of 100m/h in 10 hours
In 10 hours C, with the speed of 85.5m/h, will cover 855m

So A will beat C in 1000-855=145 meters

IMO
Ans: B

effatara · Answer

The ratio of the speeds of two moving objects is equal to the distances they travel in any given time.
Let the speeds of A, B and C be s1, s2 and s3 respectively.
Then (s1/s2)=(200/180)=10/9
 (s2/s3)=(100/95)=20/19
T/4, (s1/s3)= (20/19)*(10/9)=200/171 which means that, in the time it takes A to travel 200 meters, C will travel 171 meters. Thus, C will be able to travel (171*5)=855 meters in the time A takes to complete the 1000 meter race.
So A will beat C by 145 meters (1000-855). Ans: B

sarthak1701 · Answer

I am not sure why this approach does not work: A's distance over B in a 200m race is 20m, therefore in a 100m race his beating distance should be 10m. B's beating distance over C is 5 m in a 100 metre race.

A's 'excess' over B is 10m/per 100 m

while B's 'excess' over C is 5m/per 100m

Thus A's excess over C is 10 + 5 = 15 m/per 100 m

In a kilometer race, A will beat C by 15*10 = 150 m?

Is this approach wrong or the calculation?

Bunuel · Answer

When A is at the 100-meter mark, B is at the 90-meter mark. 
 When B is at the 100-meter mark, C is at the 95-meter mark.

However, this does NOT mean that when A is at the 100-meter mark, C is at the 85-meter mark.

When B is at the 90-meter mark, C is at 90 - (9/10) * 5 = 85.5 meters.

Thus:

When A is at the 100-meter mark, B is at 90 meters, and C is at 85.5 meters

This gives a difference of 14.5 meters between A and C over 100 meters, which scales to 145 meters over a 1,000-meter race. Therefore, A beats C by 145 meters in a kilometer race.

Answer: B.

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In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra

Prep Toolkit

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