BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

mixtures and ratio

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 am
Thanked: 17 times
Followed by:1 members

mixtures and ratio

by rahul.s » Sun Jan 31, 2010 3:13 am
Trail mix P is 15 percent cashews and 85 percent almonds by weight; trail mix R is 40 percent cashews and 60 percent peanuts. If a mixture of P and R contains 20 percent cashews, what percent of the weight of the mixture is R?

A) 15 %
B) 20 %
C) 33 1/3%
D) 50 %
E) 80 %

OA: B
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Sun Jan 31, 2010 3:35 am
rahul.s wrote:Trail mix P is 15 percent cashews and 85 percent almonds by weight; trail mix R is 40 percent cashews and 60 percent peanuts. If a mixture of P and R contains 20 percent cashews, what percent of the weight of the mixture is R?

A) 15 %
B) 20 %
C) 33 1/3%
D) 50 %
E) 80 %

OA: B
Say P and R are mixed in 1:x proportion

% of cashew in the mix =(1*15+x*40)/(1+x) = 20 => 20x = 5 => x =1/4

P&R are mixed 1:1/4 proportion

% of R in the mix = 1/4/(1+1/4) *100 = 1/5*100 = 20%
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 241
Joined: Wed Jan 27, 2010 10:10 pm
Location: Chennai
Thanked: 23 times
Followed by:2 members
GMAT Score:690

by sars72 » Sun Jan 31, 2010 5:42 am
ajith wrote:
Say P and R are mixed in 1:x proportion

% of cashew in the mix =(1*15+x*40)/(1+x) = 20 => 20x = 5 => x =1/4

P&R are mixed 1:1/4 proportion

% of R in the mix = 1/4/(1+1/4) *100 = 1/5*100 = 20%
ajith, i've forgotten all that i studied about mixtures n alligations. I am not able to follow your calculations. Could you please elaborate a bit on them? Thanks.
Last edited by sars72 on Sun Jan 31, 2010 6:23 am, edited 1 time in total.
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sun Jan 31, 2010 5:59 am
I did it this way. I'm really horrible at setting up mixture equations. So, let me try by using a non-equation approach.

Set a line for distributing cashews. M is the mixture.

[5] [20]
P ------------- M -------------------- R
(15) (20) (40)

% of R in mixture = 5/(5+20) = 5/25 = 20%
Top
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 am
Thanked: 17 times
Followed by:1 members

by rahul.s » Sun Jan 31, 2010 6:11 am
papgust wrote:% of R in mixture = 5/(5+20) = 5/25 = 20%
how'd you get that?
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sun Jan 31, 2010 6:21 am
I hope that this method could be solved for this question.

It's a weighted average concept. You could check out Stuart's method in this site. This method is the same as Stuart's.

If you are not able to search for stuart's method, check this out
https://www.beatthegmat.com/mba/2009/12/ ... art-2-of-2

------

Distance b/w P and M in the line is 5. Distance b/w M and R is 20. Total distance is 25

Weight of R is 5 [b/w P and M] and weight of P is 20 [b/w M and R]

So, R / (P+R) = 5/25
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Sun Jan 31, 2010 6:29 am
sars72 wrote: ajith, i've forgotten all that i studied about mixtures n alligations. I am not able to follow your calculations. Could you please elaborate a bit on them? Thanks.
Any proportion can be written in 1: x form Say P & R are mixed in 1: x proportion

cashew coming from mixture P = 15 (15*1 - Since the proportion is 1: x)
cashew coming from mixture R = 40x (40*x - since the proportion is 1:x)

Total amount of mixture = 1+x

The cashew % in the mixture = 15+40x/1+x and it is given as 20

And it gives x =1/4

so P& R are mixed in 1:0.25 proportion so for every 4 units of P 1 unit of R is added hence % of R in the mixture = 1/5*100 =20%
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Sun Jan 31, 2010 7:05 am
rahul.s wrote:
papgust wrote:% of R in mixture = 5/(5+20) = 5/25 = 20%
how'd you get that?
rahul its actually like this take any one component for which is common in bth and is also present in resultant
and write its % in following manner


P....................................R
15.................................40
then write the % of the same in resultant like this

15-----------------------------40
--------------20-----------------
cross diff
40-20...........................20-15
=20...........................5

now tot=20+5

the right side is for mix R
and left side is for mix P

% of R in mix is 5/25=1/4=20%

HTH
Top
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 am
Thanked: 17 times
Followed by:1 members

by rahul.s » Sun Jan 31, 2010 8:11 am
stacey's post was amazing. made weighted average problems look simple and uncomplicated. i highly recommend everyone to go through the solution

follow the link.

https://www.beatthegmat.com/mba/2009/12/ ... art-2-of-2

thanks papgust :D
Top
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 am
Thanked: 17 times
Followed by:1 members

by rahul.s » Sun Jan 31, 2010 8:15 am
thephoenix wrote:P....................................R
15.................................40
then write the % of the same in resultant like this

15-----------------------------40
--------------20-----------------
cross diff
40-20...........................20-15
=20...........................5
why is it 40 - 20 and 20 - 15?

i don't follow
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sun Jan 31, 2010 8:23 am
rahul.s wrote:
thephoenix wrote:P....................................R
15.................................40
then write the % of the same in resultant like this

15-----------------------------40
--------------20-----------------
cross diff
40-20...........................20-15
=20...........................5
why is it 40 - 20 and 20 - 15?

i don't follow
Imagine the line as a "tug of war".
40-20 = 20 is the weight of P.
20-15 = 5 is the weight of R.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Sun Jan 31, 2010 8:40 am
rahul.s wrote:
thephoenix wrote:P....................................R
15.................................40
then write the % of the same in resultant like this

15-----------------------------40
--------------20-----------------
cross diff
40-20...........................20-15
=20...........................5
why is it 40 - 20 and 20 - 15?

i don't follow
it a short cut trick
write the lower value in left most side and higher value in right most side
write the men in centre
below that write the diff of higher value and mean on left most side , and the diff of mean and lower value on right most side
this is your final ratio
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Mon Feb 01, 2010 5:09 am
thephoenix wrote:
% of R in mix is 5/25=1/4=20%

HTH
% of R in mix is 5/25 = 1/5 = 20%
Top
Post new topic Post Reply
• Page 1 of 1