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3 cooks have to make 80 burgers.They are known to make 20

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3 cooks have to make 80 burgers.They are known to make 20  [#permalink]

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New post 24 Jan 2018, 00:14
virtualanimosity wrote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?

A. 16 minutes
B. 24 mins
C. 32 mins
D. 40 mins
E. 30 mins


Let the time taken by A is \(t1 = \frac{20}{x}, t2 = \frac{60}{(y+z)}\)
Also, \(x + y + z = 20\)...
\(t1 + t2 = 80\), combing all the above equations we get \((x-10)(x-5) = 0\) or \(x =10, 5\)
But when we substitute \(x = 5\) in \(t1 = 20/x\) we get t1 = 2 but t1 is greater than 3, so \(t1 = 4\).
Hence, C.
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Re: 3 cooks have to make 80 burgers.They are known to make 20  [#permalink]

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New post 13 Sep 2018, 20:06
virtualanimosity wrote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?

A. 16 minutes
B. 24 mins
C. 32 mins
D. 40 mins
E. 30 mins


a plane and very simple solution

Answer: Option C
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Re: 3 cooks have to make 80 burgers.They are known to make 20  [#permalink]

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New post 13 Sep 2018, 20:08
virtualanimosity wrote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?

A. 16 minutes
B. 24 mins
C. 32 mins
D. 40 mins
E. 30 mins


Answer: Option C

Please check atachment for solution
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Screen Shot 2018-09-14 at 9.35.05 AM.png [ 458.89 KiB | Viewed 463 times ]


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Re: 3 cooks have to make 80 burgers.They are known to make 20  [#permalink]

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New post 10 Dec 2018, 09:25
virtualanimosity wrote:
3 cooks have to make 80 burgers.They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?

A. 16 minutes
B. 24 mins
C. 32 mins
D. 40 mins
E. 30 mins




I copied bml explanation to make the initial explanation easy for me houston1980.



bml wrote:
let the rates be x,y,z
\(\frac{20}{x+y+z} = 1\)
we know x+y+z = 20 and \(\frac{20}{x}+\frac{60}{y+z} = 8\)
putting (y+z) = (20-x) we get

\(x^2-15x+50=0\)
solving we get x= 5,10; x cannot be 10 because \(\frac{20}{x}>3\)

so to prepare 160 burgers, time reqd. = \(\frac{160}{5}=32\)

nice expl.n rohansherry
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Re: 3 cooks have to make 80 burgers.They are known to make 20  [#permalink]

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Re: 3 cooks have to make 80 burgers.They are known to make 20   [#permalink] 28 Dec 2019, 04:56

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