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A grocer has 400 pounds of coffee in stock, 20 percent
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kanusha
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A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  Updated on: 25 Jul 2014, 22:06
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A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%
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Originally posted by kanusha on 25 Jul 2014, 21:51.
Last edited by Gnpth on 25 Jul 2014, 22:06, edited 2 times in total.
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  27 Jul 2014, 03:45
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1. 20% of 400=80 pounds of decaffeinated coffee
2. 60% of 100=60 pounds of decaffeinated coffee
3. Wt have 140 pounds of decaffeinated out of 500 pounds, that means 140/500*100%=28%. The correct answer is A.
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  25 Jul 2014, 21:54
1 , 20% of 400 mean 320 , Next 60% of 100 mean 40 … so on total 360 is the coffee Out of total 500 pounds of coffee. 500 is 100% , 360 pounds = ?%..... 3600/500 = 72% is Original it mean 28%is Decaffeinated. So A

2, Using multipliers… 20% mean 0.2 60% mean 0.6 …. So multiplying both the multipliers 0.12 ??

Can anyone solve this using multipliers as approach?
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  27 Jul 2014, 03:47
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kanusha wrote:
1 , 20% of 400 mean 320 , Next 60% of 100 mean 40 … so on total 360 is the coffee Out of total 500 pounds of coffee. 500 is 100% , 360 pounds = ?%..... 3600/500 = 72% is Original it mean 28%is Decaffeinated. So A

2, Using multipliers… 20% mean 0.2 60% mean 0.6 …. So multiplying both the multipliers 0.12 ??

Can anyone solve this using multipliers as approach?



Kanusha, never mix percents if you take them from different numbers!

In this case decaffeinated coffee= 0.2*400+0.6*100=140. So, again 140/500*100%=28%.
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  20 Dec 2017, 11:28
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kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%


Since the grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated, 0.2 x 400 = 80 pounds are decaffeinated.

Since the grocer buys another 100 pounds of coffee, 60 percent of which is decaffeinated, the grocer has 60 more pounds of decaffeinated coffee.

Thus, the percentage of decaffeinated coffee is (80 + 60)/(400 + 100) = 140/500 = 28/100 = 28%.

Answer: A
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  20 Dec 2017, 11:55
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This can be thought of in terms of weighted averages.

the initial coffee is 400 pounds and the latter coffee is 100 pounds so the first gets a weight of 4/5 and the latter gets a weight of 1/5.

20(4/5)+60(1/5)=

16+12=

28
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  27 Dec 2017, 13:29
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Alternate method: Alligation method

400 pounds (20%) 100 Pounds (60%) {qty 4:1}

{Difference in ratio is 60-20=40% ==> Concentration will be in reverse ratio ==> 1:4 ==> 1/5*40=8 or 4/5*40=32}

Answer : 20+8 or 60-32 = 28%
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  15 Oct 2018, 11:12
20% of 400 is decaf

20% * 400 = 80

60% of 100 is decaf

60% * 100 = 60

(80 + 60) = 140

Total pounds of coffee = 400 + 100 = 500

\(\frac{140}{500}\) (multiply both by 2 to make easier to deal with as a percentage) = \(\frac{28}{100}\) = 28%

Answer choice A
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  05 Jan 2019, 00:33
20% of 400 is decaffeinated

20% * 400 = 80

60% of 100 is decaffeinated

60% * 100 = 60

(80 + 60) = 140

Total pounds of coffee = 400 + 100 = 500

500 * decaffeinated / 100 = 140
5 * decaffeinated = 140
decaffeinated = 28 %

Answer choice A
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  27 Aug 2019, 02:57
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%


Dear VeritasKarishma

How can I apply the concentration method here? I tried but fails. I hope you can help please.

Thanks in advance
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VeritasKarishma
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  28 Aug 2019, 03:27
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kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%



It is a weighted average problem.

Concentration of decaf in original inventory = 20%
Concentration of decaf in new inventory = 60%

Concentration of decaf in mix = ?

w1/w2 = (A2 - Aavg)/(Aavg - A1)

400/100 = (60 - Aavg)/(Aavg - 20)

4*Aavg - 80 = 60 - Aavg

Aavg = 28%

Answer (A)

Check here: https://www.veritasprep.com/blog/2011/0 ... -mixtures/
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  28 Aug 2019, 03:31
VeritasKarishma wrote:
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%



It is a weighted average problem.

Concentration of decaf in original inventory = 20%
Concentration of decaf in new inventory = 60%

Concentration of decaf in mix = ?

w1/w2 = (A2 - Aavg)/(Aavg - A1)

400/100 = (60 - Aavg)/(Aavg - 20)

4*Aavg - 80 = 60 - Aavg

Aavg = 28%

Answer (A)

Check here: https://www.veritasprep.com/blog/2011/0 ... -mixtures/


Thanks VeritasKarishma for your keen reply and response. But can I apply the following formula for the problem at hand:

c1 * v1 = c2 * v2

Thanks
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  29 Jan 2020, 03:02
400/100 = (60 - X)/(X-20) => 4X - 80 = 60 - X; X = 28%
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A grocer has 400 pounds of coffee in stock, 20 percent [#permalink] New post  21 Aug 2020, 08:13
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%


Here is a one line solution using weighted average concept:

Average % (decaffeinated) = (400/500)*20% + (100/500)*60% ---------(where 400/500 = wt. of 1st coffee-type, 100/500 = wt. of 2nd coffee-type)
= (4/5)*20% + (1/5)*60%
= 16% + 12%
= 28%
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