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# A 2 Part question

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01 Jan 2013, 22:48
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Hello friend,

Please try this 2 part question...

A can beat B in a 400 yards race by 60 yards, B can beat C in a 850 yards race by 100 yards, whereas C can beat D in a 600 yards race by 40 yards. Select the values of 'A beats C', & 'B beats D' by yards in a 200 yards race in the table that are consistent with the information provided.
Make only two selections, one in each column.

-Shalabh
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Re: A 2 Part question [#permalink]

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03 Jan 2013, 18:50
This is the longer version of solution , there is a quick way to do it also :

Lets say As is the speed of A , Bs is the speed of B and similarly Cs is for C & Ds is for D.

if A took T1 time to finish the 400 yards race , so in the same time B will cover 340 yards

Therefore, we can say that T1 = 400/As and T1 = 340/Bs (Speed = Distance/Time or Time = Distance/speed ).

T1 = 400/As = 340/Bs => As/Bs = 400/340 or As/Bs = 20/17

Similarly , we can get

Bs/Cs = 17/15 & Cs/Ds= 15/14

therefore we can say , As/Cs = 4/3 ( As = 20/17 * Bs = 20/17 * 17/15 * Cs = 20/15 Cs

Lets assume to complete a 200 yards race A took time T , then

As=200/T or T = 200/As , in the same time C will cover X distance , so X = Cs * T (Distance = Speed * time)

Therefore X = Cs * 200/As ( from above we knw that As/Cs = 4/3 )

X = 200 / (As/Cs) = 200 / (4/3) = 150.

Thereby we can say that A will beat C in a 200 yards race by 50 yards.

Similarly we can get that B will beat D in a 200 yards race by 35 yards.
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Re: A 2 Part question [#permalink]

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04 Jan 2013, 01:19
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Expert's post
punwish wrote:
This is the longer version of solution , there is a quick way to do it also :

Lets say As is the speed of A , Bs is the speed of B and similarly Cs is for C & Ds is for D.

if A took T1 time to finish the 400 yards race , so in the same time B will cover 340 yards

Therefore, we can say that T1 = 400/As and T1 = 340/Bs (Speed = Distance/Time or Time = Distance/speed ).

T1 = 400/As = 340/Bs => As/Bs = 400/340 or As/Bs = 20/17

Similarly , we can get

Bs/Cs = 17/15 & Cs/Ds= 15/14

therefore we can say , As/Cs = 4/3 ( As = 20/17 * Bs = 20/17 * 17/15 * Cs = 20/15 Cs

Lets assume to complete a 200 yards race A took time T , then

As=200/T or T = 200/As , in the same time C will cover X distance , so X = Cs * T (Distance = Speed * time)

Therefore X = Cs * 200/As ( from above we knw that As/Cs = 4/3 )

X = 200 / (As/Cs) = 200 / (4/3) = 150.

Thereby we can say that A will beat C in a 200 yards race by 50 yards.

Similarly we can get that B will beat D in a 200 yards race by 35 yards.

Hi punwish,

That's the correct answer. Yes, you are right this is a longer method to approach the question. I think the approach below is smarter one.

We can find out the continued ratios of all 4 players.

--A--:---B--:---C--:---D----
400 : 340
------:850 : 750
------:-----: 600 : 560
------------------------------------
400 : 340 : 750/850*340 : --
400 : 340 : 300 : 560/600*300
400 : 340 : 300 : 280

So. we can infer that A beats C by 100 yards in a 400 yard race, so it will beat C by 50 yards in a 200 yard race.

Similarly, we can infer that B beats D by 60 yards in 340 yard race, so it will beat D by (340-280)/340*200 = ~35 yards in a 200 yard race.

Meanwhile, don't forget to attend the SC session on Saturday. Please find the link below:

-Shalabh
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Re: A 2 Part question [#permalink]

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08 Jan 2013, 22:26
50 and 35
just find out by how much each beats other in 200yards race...
easy one....
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Re: A 2 Part question [#permalink]

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08 Jan 2013, 22:49
egmat wrote:
--A--:---B--:---C--:---D----
400 : 340
------:850 : 750
------:-----: 600 : 560
------------------------------------
400 : 340 : 750/850*340 : --
400 : 340 : 300 : 560/600*300
400 : 340 : 300 : 280

That was a very quick method Shalabh. Thanks!
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Re: A 2 Part question [#permalink]

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08 Jan 2013, 23:21
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Expert's post
Shashank3016 wrote:
egmat wrote:
--A--:---B--:---C--:---D----
400 : 340
------:850 : 750
------:-----: 600 : 560
------------------------------------
400 : 340 : 750/850*340 : --
400 : 340 : 300 : 560/600*300
400 : 340 : 300 : 280

That was a very quick method Shalabh. Thanks!

Thank you Shashank. By the way do not forget to attend following event this weekend to learn how to improve by up to 70 points in 25 days. Pl. click to know more.

-Shalabh Jain
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Re: A 2 Part question   [#permalink] 08 Jan 2013, 23:21
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# A 2 Part question

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