GMAT Changed on April 16th - Read about the latest changes here

 It is currently 26 May 2018, 06:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Mar 2015
Posts: 80
in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

06 Feb 2018, 10:34
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

44% (02:39) correct 56% (02:34) wrong based on 34 sessions

### HideShow timer Statistics

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
Intern
Joined: 15 May 2012
Posts: 24
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

06 Feb 2018, 18:23
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)
Math Expert
Joined: 02 Aug 2009
Posts: 5783
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

07 Feb 2018, 03:21
Expert's post
2
This post was
BOOKMARKED
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Manager
Joined: 01 Jun 2015
Posts: 236
Location: India
GMAT 1: 620 Q48 V26
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

07 Feb 2018, 09:38
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 ??
Math Expert
Joined: 02 Aug 2009
Posts: 5783
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

07 Feb 2018, 09:57
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Manager
Joined: 01 Jun 2015
Posts: 236
Location: India
GMAT 1: 620 Q48 V26
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

07 Feb 2018, 10:23
Thank you.The wording was little confusing.Could this type of question appear on gmat?
Intern
Joined: 30 Dec 2015
Posts: 3
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge [#permalink]

### Show Tags

08 Feb 2018, 14:38
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
Re: in a race, amit gave rahul a head start of 'x' m and took 20 sec to ge   [#permalink] 08 Feb 2018, 14:38
Display posts from previous: Sort by