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

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In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra  [#permalink]

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New post 11 Apr 2019, 05:12
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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

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In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra  [#permalink]

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New post 11 Apr 2019, 06:25
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nm97 wrote:
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


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
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In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra  [#permalink]

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New post 11 Apr 2019, 06:44
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nm97 wrote:
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


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
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Re: In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra  [#permalink]

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New post 20 Apr 2019, 01:03
1
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
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Re: In a 200 meters race, A beats B by 20 meters, while in a 100 meters ra   [#permalink] 20 Apr 2019, 01:03
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