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# If the farmer sells 75 of his chickens, his stock of feed

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If the farmer sells 75 of his chickens, his stock of feed [#permalink]  25 Oct 2009, 01:41
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If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300
[Reveal] Spoiler: OA

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Re: Feeding the Chickens [#permalink]  25 Oct 2009, 11:35
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slingfox wrote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300

# of chickens - x
# of days - d

If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals xd=(x-75)(d+20);
If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals xd=(x+100)(d-15).

(x-75)(d+20)=(x+100)(d-15) --> \frac{d+20}{d-15}=\frac{x+100}{x-75} --> x=5d

xd=(x-75)(d+20) --> 5d^2=(5d-75)(d+20) --> d^2=(d-15)(d+20) --> d=60 --> x=5d=300.

Hope it helps.
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Re: Feeding the Chickens [#permalink]  06 Dec 2010, 05:34
Bunuel, I have tried a different approach. Can you please explain why it didn't work? Thank you.

x ... number of chickens
k ... 1 chicken consumption per day
T ... total number of days for x chickens to live given their current number

We get the following equations:

(y - 75)/k = T +20
(y + 100)/k = T - 15
y/k = T

However, I couldn't solve the equations. I got k = 5. But substituting 5 into the equation, I couldn't solve it.

Thank you.
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Re: Feeding the Chickens [#permalink]  06 Dec 2010, 08:03
4
KUDOS
Expert's post
slingfox wrote:
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?

A. 60
B. 120
C. 240
D. 275
E. 300

or you can make your equations in this way: Let us say he has planned for d days for c chickens. According to the question,

the food 75 chicken consumed in d days will last 20 days if consumed by (c - 75) chickens
So 75d = (c - 75)20 ..... (I)

What c chickens consumed in 15 days, 100 chickens will consume in (d - 15) days
15c = 100(d - 15) ......(II)

Solve I and II to get c = 300
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews SVP Joined: 09 Sep 2013 Posts: 2393 Followers: 196 Kudos [?]: 38 [0], given: 0 Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink] 27 Sep 2013, 08:10 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Status: Joining Cranfield Sep 2014 Joined: 01 Sep 2012 Posts: 65 Concentration: Technology, General Management GMAT 1: 530 Q50 V14 GMAT 2: 630 Q48 V29 WE: Engineering (Energy and Utilities) Followers: 0 Kudos [?]: 19 [0], given: 60 Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink] 19 Oct 2013, 04:42 bumpbot wrote: Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Let Number of Chickens be X The number of days chicken will eat a fixed stock will be inversely proportional to number of chickens. Hence if number of days X chicken will eat the stock will be D = K/ X If number of chicken is reduced by 75 then D+20 = K / (X-75) If number of chicken is increaded by 100 then D-15 = K / (X+100) Replacing D=K/X in above two equations:- K/X + 20 = K / (X-75) K/X - 15 = k / (X+100) solving above two equations gives X =300. Answer is E Intern Joined: 10 Oct 2013 Posts: 2 Location: India Concentration: International Business, Technology GMAT Date: 11-11-2013 WE: Business Development (Manufacturing) Followers: 0 Kudos [?]: 5 [0], given: 43 Re: Feeding the Chickens [#permalink] 02 Nov 2013, 09:41 Bunuel wrote: slingfox wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? A. 60 B. 120 C. 240 D. 275 E. 300 # of chickens - x # of days - d If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals xd=(x-75)(d+20); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals xd=(x+100)(d-15). (x-75)(d+20)=(x+100)(d-15) --> \frac{d+20}{d-15}=\frac{x+100}{x-75} --> x=5d xd=(x-75)(d+20) --> 5d^2=(5d-75)(d+20) --> d^2=(d-15)(d+20) --> d=60 --> x=5d=300. Answer: E (300) Hope it helps. Thank you for the explanation Bunuel. However, I do not understand something here: How does multiplying the number of days (d) with the number of chickens (x) give the amount of feed the farmer has ? Shouldn't it rather be the amount of feed the chickens consume in one d days ? Math Expert Joined: 02 Sep 2009 Posts: 27397 Followers: 3487 Kudos [?]: 26177 [1] , given: 2706 Re: Feeding the Chickens [#permalink] 03 Nov 2013, 10:39 1 This post received KUDOS Expert's post nishantsharma87 wrote: Bunuel wrote: slingfox wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? A. 60 B. 120 C. 240 D. 275 E. 300 # of chickens - x # of days - d If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals xd=(x-75)(d+20); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals xd=(x+100)(d-15). (x-75)(d+20)=(x+100)(d-15) --> \frac{d+20}{d-15}=\frac{x+100}{x-75} --> x=5d xd=(x-75)(d+20) --> 5d^2=(5d-75)(d+20) --> d^2=(d-15)(d+20) --> d=60 --> x=5d=300. Answer: E (300) Hope it helps. Thank you for the explanation Bunuel. However, I do not understand something here: How does multiplying the number of days (d) with the number of chickens (x) give the amount of feed the farmer has ? Shouldn't it rather be the amount of feed the chickens consume in one d days ? That's because the amount of feed each chicken eats a day, say z, can be reduced on both sides: zxd=z(x-75)(d+20) --> xd=(x-75)(d+20); zxd=z(x+100)(d-15) --> xd=(x+100)(d-15). Hope it's clear. _________________ Intern Joined: 10 Oct 2013 Posts: 2 Location: India Concentration: International Business, Technology GMAT Date: 11-11-2013 WE: Business Development (Manufacturing) Followers: 0 Kudos [?]: 5 [0], given: 43 Re: Feeding the Chickens [#permalink] 04 Nov 2013, 10:07 Thank you for the explanation as always Bunuel! I find such word problems, where we have to assume some constants/variable to solve the question (that cancel out before the final solution arrives) and ALSO infer its relationship with the variables/constants given in the word problem, quite tricky (specially WORK/RATE problems! ) It'll be very helpful if you can provide some similar questions or content (or their link) to practice. Cheers! Manager Joined: 10 Mar 2013 Posts: 200 Followers: 0 Kudos [?]: 7 [0], given: 1737 Re: Feeding the Chickens [#permalink] 29 Dec 2013, 18:58 Bunuel wrote: slingfox wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? A. 60 B. 120 C. 240 D. 275 E. 300 # of chickens - x # of days - d If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned --> Amount of feed equals xd=(x-75)(d+20); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned --> Amount of feed equals xd=(x+100)(d-15). (x-75)(d+20)=(x+100)(d-15) --> \frac{d+20}{d-15}=\frac{x+100}{x-75} --> x=5d xd=(x-75)(d+20) --> 5d^2=(5d-75)(d+20) --> d^2=(d-15)(d+20) --> d=60 --> x=5d=300. Answer: E (300) Hope it helps. Wow! When I first saw this question, I had no clue even how to begin. Bunuel, where in the problem suggests that one should take this approach? Verbal Forum Moderator Joined: 15 Jun 2012 Posts: 1062 Location: United States Followers: 121 Kudos [?]: 1268 [0], given: 119 Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink] 30 Dec 2013, 03:11 slingfox wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? A. 60 B. 120 C. 240 D. 275 E. 300 This question is similar to work-rate questions. The key is always calculate how much work each person/machine does in 1 unit of time. For this question, we have: number of chickens = X stock feed = T (days) It means X chickens can be fed in T days --> 1 chicken eats in 1 day = 1/(XT) 1st scenario, we sell 75 chickens, we have number of chickens = X - 75 stock feed = T + 20 (days) --> 1 chicken eats 1 day = 1/[(X-75)(T+20)] Because the amount of food each chicken eats in 1 day is the same: --> 1/XT = 1/[(X-75)(T+20)] --> XT = XT+ 20X - 75T - 1500 --> 20X - 75T - 1500 = 0 2nd scenario: we buy 100 chickens number of chickens = X + 100 stock feed = T - 15 (days) --> 1 chicken eats 1 day = 1/[(X+100)(T-15)] Because the amount of food each chicken eats in 1 day is the same: --> 1/XT = 1/[(X+100)(T-15)] --> XT = XT -15X +100T - 1500 --> 15X +100T - 1500 = 0 Solve 2 equations 20X - 75T - 1500 = 0 15X +100T - 1500 = 0 Clearly, X = 300 Hence, E is correct. We have _________________ Please +1 KUDO if my post helps. Thank you. "Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong." Chris Bangle - Former BMV Chief of Design. SVP Joined: 06 Sep 2013 Posts: 1661 Location: United States Concentration: Finance GMAT 1: 710 Q48 V39 WE: Corporate Finance (Investment Banking) Followers: 12 Kudos [?]: 164 [1] , given: 268 Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink] 18 Feb 2014, 15:50 1 This post received KUDOS Its quite a journey but here we go. (q-75)(t+20) and (q+100)(t-15). Now we need to equal each to qt. So we will have 20q - 75t - 75(20) on the first equation and -15q + 100t - 100(15) on the second equation. We could simplify some terms but the point is we need to find 'q' so anyways after simplifying we can multiply the first equation by 3 and we're left with 12q - 60t -75 *(4) *(4) and multiply the second by 3 to get -9q + 60t - 100 (3)*3. So then we finally get to 3q = 900, q = 300 E is the answer If any one comes up with a fast way to do this I'll def provide some Kudos Cheers! J Re: If the farmer sells 75 of his chickens, his stock of feed [#permalink] 18 Feb 2014, 15:50 Similar topics Replies Last post Similar Topics: 1 If a farmer sells 15 of his chickens, his stock of feed will 1 12 Dec 2012, 12:43 1 If a farmer sells 15 of his chickens, his stock of feed will 3 01 May 2012, 13:53 2 A farmer spent$35 on feed for chickens and goats. He spent 5 21 Apr 2012, 09:03
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