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in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge
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prince00113
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in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  06 Feb 2018, 09:34
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in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24
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alnewton
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  06 Feb 2018, 17:23
Amit Speed -- 5s
Rahul Speed -- 4s

Relative speed (Because they are going in same direction) = 5s - 4s =s

Time taken by Amit to reach 2x --> 2x / s = 20 => x/s = 10

Time taken by Amit to overtake --> x/s = 10

Now,
Rahul finishes the race in 60 sec, so Amit, because he is faster will finish in less time --> 4/5 * 60 = 48 sec.

The ration of distances will be proportional to the ratio time thus

Ration = 10/48 --> 5/24 (B)
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chetan2u
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  07 Feb 2018, 02:21
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prince00113 wrote:
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24



Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B
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techiesam
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  07 Feb 2018, 08:38
chetan2u wrote:
prince00113 wrote:
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24



Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B


chetan2u

I have applied the same reasoning but I concluded that Amit traveled (x+y) m.And my final answer was 5/12.

<-----Amit----><------Rahul------>
---------------------------------------
<-------y------>/<-----------x------->

Can you please explain why Amit traveled 2x+y ??
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chetan2u
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  07 Feb 2018, 08:57
Expert Reply
techiesam wrote:
chetan2u wrote:
prince00113 wrote:
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24



Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B


chetan2u

I have applied the same reasoning but I concluded that Amit traveled (x+y) m.And my final answer was 5/12.


---------------------------------------
/

Can you please explain why Amit traveled 2x+y ??



Hi..
Rahul is x ahead of Amit, but then in 20 secs, goes ahead of Rahul by x..
So if Rahul travelled y...
Position at start..
A.....<--x--->.....R
In 20 secs..
|<--x-->|<--y-->|R|<--x-->A
So R traveled y, while A traveled x+y+x
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techiesam
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  07 Feb 2018, 09:23
Thank you.The wording was little confusing.Could this type of question appear on gmat?
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BYZ
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  08 Feb 2018, 13:38
let A be the speed of Amit and R be the speed of Raul
the speed of R is 1/60 (fraction of race/sec)
there for the speed of A is 1/48
Amit took 10sec to catch up to Raul and 10 more seconds to beat him by x meters
therefore the total distance the Raul travelled would be: 10/48 = 5/24
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Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink] New post  18 Feb 2021, 11:03
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