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A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe

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A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post Updated on: 06 Feb 2017, 19:49
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Question Stats:

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A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%





Source - Manhattan Review GMAT Quant

Originally posted by ssr300 on 04 Feb 2017, 18:55.
Last edited by ssr300 on 06 Feb 2017, 19:49, edited 1 time in total.
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post 04 Feb 2017, 21:11
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sharma123 wrote:
ssr300 wrote:
A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%





Source - Manhattan Review GMAT Quant

i think answer is B 12.5%

let price of 100gms peanuts be 100
so price of 100 gms mix = 110(20 gms peanut + 80 gms cashw)
now 500 gms mix will be 550(100 gms peanut+400 gms cashew)
as we know price of 100 gms peanut is 100; price of 400 gms cashew is 450
so (450/400)*100=112.5
12.5% more than price of 100 gm peanuts

chetan2u can you please correct me if im wrong also if there is any simpler method to solve


Hi,

You are absolutely correct with your method..

A faster, may be slightly more logical, way would be...
80% cashew is making a difference of 10%, so 100% cashew will make a difference of\(\frac{100*10}{80}\)=12.5%
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post 04 Feb 2017, 20:11
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ssr300 wrote:
A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%





Source - Manhattan Review GMAT Quant

i think answer is B 12.5%

let price of 100gms peanuts be 100
so price of 100 gms mix = 110(20 gms peanut + 80 gms cashw)
now 500 gms mix will be 550(100 gms peanut+400 gms cashew)
as we know price of 100 gms peanut is 100; price of 400 gms cashew is 450
so (450/400)*100=112.5
12.5% more than price of 100 gm peanuts

chetan2u can you please correct me if im wrong also if there is any simpler method to solve
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post 04 Feb 2017, 20:20
2
[quote="ssr300"]A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%




let price of peanut per gm be "P" and cashew "C"
now
20P + 80C =total cost of mixture(Let total quantity be 100 gm)----1

According to question it is given that "mixture costs 10 percent more than the cost of an equal quantity of pure peanuts"
100gm mixture will cost 110P---2

20P+80C = 110p
80C = 90P----3
we have to find by what percent cashew more expensive than peanuts,so basically we need to get C-P/P *100
From 3 we can get 8C =9P
C/P = 9/8
C/P-1=9/8-1
((C-P)/P)*100=1/8*100 = 12.5%
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post 06 Feb 2017, 17:16
A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%

if mix 1 contains 100 peanuts and costs $1.00,
then 1 peanut costs $1.00/100=1¢
if mix 2 contains 20 peanuts and 80 cashews and costs $1.10,
then 1 cashew costs [$1.1-(20*1¢)]/80=1.125¢
1.125-1=.125
.125/1=12.5% cost increase from peanuts to cashews
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe  [#permalink]

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New post 06 Mar 2018, 10:30
ssr300 wrote:
A nut mix contains, by weight, 20 percent peanuts and 80 percent cashews. If this mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A) 10.0%
B) 12.5%
C) 15.0%
D) 22.5%
E) 25.0%


We can assume that are 10 lbs of mixed nuts; so there are 2 lbs of peanuts and 8 lbs of cashews. We can also assume that the peanuts cost $10 per pound; so the mixed nuts cost $11 per pound. Now if we let c = the cost of cashews, we have:

2(10) + 8c = 10(11)

20 + 8c = 110

8c = 90

c = 90/8 = 45/4 = 11.25

Thus, the cashews are (11.25 - 10)/10 = 1.25/10 = 0.125 = 12.5% more expensive than the peanuts.

Answer: B
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Re: A nut mix contains, by weight, 20 percent peanuts and 80 percent cashe &nbs [#permalink] 06 Mar 2018, 10:30
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