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How many workers problem!

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Manager
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Joined: 18 Jun 2011
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How many workers problem! [#permalink] New post 19 Jun 2011, 22:31
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A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1250. How many workers were part of the latter production run?

A)6
B)10
C)11
D)15
E)23.5
[Reveal] Spoiler: OA
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Re: How many workers problem! [#permalink] New post 20 Jun 2011, 03:27
guygmat wrote:
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1250. How many workers were part of the latter production run?

A)6
B)10
C)11
D)15
E)23.5


The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1

5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1250 .. thus for the current period = 1250 -500 = 750
(5n+45)K= 750
k = 750/5n+45........................................2

equate 1 and 2

500/5n+20 = 750 /5n+45
500(5n+45) = 750(5n+20)

2500n + 22500 = 3750n + 15000
-1250n = -7500
n = 6

thus n+5 = 11

hence C
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Re: How many workers problem! [#permalink] New post 21 Jun 2011, 19:15
Expert's post
guygmat wrote:
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1250. How many workers were part of the latter production run?

A)6
B)10
C)11
D)15
E)23.5


In first k days,
(5n + 20)*k = 500
5nk + 20k = 500 ....(I)

In the next k days,
(5(n+5) + 20)*k = 750
5nk + 45k = 750 ....(II)

Look at equations I and II.
The only difference on LHS is 25k which is offset on RHS by 250
So 25k = 250 or k = 10
Put k = 10 in any one equation above to get n = 6.
New number of workers = 6 + 5 = 11
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Re: How many workers problem! [#permalink] New post 22 Jun 2011, 04:39
good explanation, regards
Re: How many workers problem!   [#permalink] 22 Jun 2011, 04:39
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