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A marzipan factory has two machines producing marzipan. Ever

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A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post Updated on: 30 Jul 2012, 04:44
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A
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C
D
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A marzipan factory has two machines producing marzipan. Every day, the two machines operate constantly from 08:00 to 18:00, and produce together N kg of marzipan. What percent of the total amount of marzipan produced by machines W and D together was produced by machine W?

(1) Working alone, it takes machine W twenty five hours to produce (N/2) kg of marzipan.

(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

Originally posted by superpus07 on 29 Jul 2012, 14:29.
Last edited by superpus07 on 30 Jul 2012, 04:44, edited 1 time in total.
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Re: A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post 30 Jul 2012, 02:48
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1
superpus07 wrote:
A marzipan factory has two machines producing marzipan. Every day, the two machines operate constantly from 08:00 to 18:00, and produce together N kg of marzipan. What percent of the total amount of marzipan produced by machines W and D together was produced by machine W?

(1) Working alone, it takes machine W twenty five hours to produce (N/2) kg of marzipan.

(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.


Denote by W the rate of machine W, and by D the rate of machine D. We know that 10W+10D=N.
We have to find the ratio \(\frac{10W}{N}\).

(1) We are given the rate of W, specifically \(W=\frac{N/2}{25}=\frac{N}{50}\). So, the ratio we are asked to find is \(\frac{10*N/50}{N}=\frac{1}{5}\).
Sufficient.

(2) From what is given, we can deduce that the rate of machine D is 4 times that of machine W. We can again find the rate of machine W, as 10(W+4W)=N, so \(W=\frac{N}{50}\).
Then we can proceed as in (1).
Again, sufficient.

Answer D (not C, as posted).
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Re: A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post 06 Aug 2012, 23:24
Hi,

(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

how is option B sufficient? it doesn't state anything about the time for either machine W or machine D; it only compares the work of two machines.

I feel answer should be A.

thanks,
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Re: A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post 07 Aug 2012, 01:46
kartik222 wrote:
Hi,

(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

how is option B sufficient? it doesn't state anything about the time for either machine W or machine D; it only compares the work of two machines.

I feel answer should be A.

thanks,


We know that 10W+10D=N. (a)
We have to find the ratio \(\frac{10W}{N}\).

(2) From what is given, we can deduce that the rate of machine D is 4 times that of machine W. We can again find the rate of machine W, using equation (a) from above: 10(W+4W)=N, so \(W=\frac{N}{50}\). Then, \(\frac{10W}{N}=10*\frac{1}{50}=\frac{1}{5}\).

Therefore, sufficient.
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Re: A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post 10 Aug 2012, 05:27
2
superpus07 wrote:
A marzipan factory has two machines producing marzipan. Every day, the two machines operate constantly from 08:00 to 18:00, and produce together N kg of marzipan. What percent of the total amount of marzipan produced by machines W and D together was produced by machine W?

(1) Working alone, it takes machine W twenty five hours to produce (N/2) kg of marzipan.

(2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.


If you understand your work-rate concepts well, you can do this without any calculations.

Given: W and D take 10 hrs to complete 1 work (N kg of Marzipan) together. So we know their combined rate of work. If you recall your work rate theory, rates are additive.
Rate of W + Rate of D = Combined Rate
If we get the rate of work of one of the machines, we can easily find the rate of work of the other.

Required: Amount of work done by W/Amount of work done together = Rate of work of W/Combined Rate

Stmnt 1: W takes 25 hrs for 1/2 work.
We now know the rate of work of W. We also have the combined rate. So we have the required ratio

Stmnt 2: To do 1/2 work, W takes twice the time taken by D to do 1 work.
So W takes 4 times the time taken by D to do one work. Since we have ratio of time taken, we get ratio of rates and hence the required rate.

(If you are wondering how,
Ratio of time taken by W:D = 4:1 so rate of work of W:D = 1:4
Rate of work of W/Combined Rate = 1/(1+4) = 1/5)

Answer (D)
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Re: A marzipan factory has two machines producing marzipan. Ever  [#permalink]

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New post 03 Mar 2019, 23:59
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Re: A marzipan factory has two machines producing marzipan. Ever   [#permalink] 03 Mar 2019, 23:59
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