ratio

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Thu Sep 01, 2011 2:58 pm

A total of $212.50 is divided among Adam, Bill and Chan such that for every dollar that Adam gets, Bill gets 75 cents and for every dollar that Bill gets, Chan gets 50 cents. Find the amount received by Chan.

D. $40

A. $32

b. $37.5

C. $35

E. $42

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Source: Beat The GMAT — Problem Solving | Thu Sep 01, 2011 2:58 pm

jarmitage23: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Jun 26, 2011 6:17 pm

by jarmitage23 » Thu Sep 01, 2011 7:39 pm

1. Bill (b) gets 75 cents for every dollar Adam (a) gets, b=.75a
2. Chan (c) gets 50 cents for every dollar Bill gets, c=.5b
3. Manipulate b=.75a into a=1.33b
4. We are told that together they have $212.50, so a+b+c = 212.5
5. The ratios have all been placed in terms of b; therefore, plug 1.33b in for a, and plug .5b in for c. Now the equation looks like this - 1.33b+b+.5b = 212.5
6. Solving for b you find out that Bill has $75. Since Chan has one half as much as Bill then he has $37.50, answer b

Hope this helps

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jbivins: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Aug 30, 2011 7:55 pm; Thanked: 1 times

by jbivins » Thu Sep 01, 2011 7:51 pm

I thought this one was fun

I was thinking the original ratio would be

A:B:C=x:.75x:Chan's part
=212.5

but chan's was hard to figure out since it was half of every dollar bill got

so lets multiple the ratio and equation by 4 to get the .75 in a whole number! Then it is easy to figure out chan's ration
4x+3x+1.5x=850
8.50x=850 !whoa what easy numbers! It's nice when you find a trick

x=100
[spoiler]Chan's amount =150....divide by 4 to get the real amount

chans amount = 150/4=37.50[/spoiler]

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Fri Sep 02, 2011 8:05 am

@jb
I could not understand your logic. please elaborate more.

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Fri Sep 02, 2011 8:56 am

Rupsk, you can work with whichever method you are comfortable.

Let Adam's share=a

Bill's share will=b=0.75a (Since he recvs 0.75 for every dollar Adam gets, Bill's total amount will=0.75 times Adam's total amount)

Chan's share=c=0.5b
Substituting the value of b=0.75a we get
c=0.5*0.75a

And if we add all three ppl's share the total is $212.50
a+b+c=$212.50
a+0.75a+0.5*0.75a=212.50
2.125a=212.50

a=100

Chan's share is 0.5*0.75a=0.375*100=37.5 Hence [spoiler]B[/spoiler]

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Fri Sep 02, 2011 2:14 pm

rupsk wrote:@jb
I could not understand your logic. please elaborate more.

A - Adam
B - Bill
C - Chan

When A receives 1 dollars.. B Receives 0.75 dollars or (3/4)X dollars.

Therefore for B to receive 1 dollar, A should receive (4/3)
or we can also say when B receives 2 dollar, A receives 8/3 dollar [ Keep this line in mind]
-- point 1

Also, when B receive 1 dollar, C receives (1/2) dollars
or, when B receives 2 dollars, C receives 1 dollar -- point 2

From Point 1 & 2 we get our ratio

(8/3):2:1

or 8:6:3

Therefore: C's share = (3/17)*212.50 = 37.50

Option B

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Fri Sep 02, 2011 2:47 pm

thank u all

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