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A large auto concern that employs 1,000 workers pays each of these wor

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A large auto concern that employs 1,000 workers pays each of these wor  [#permalink]

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New post 22 Jan 2018, 01:28
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A large auto concern that employs 1,000 workers pays each of these workers $4 per hour for the first 40 hours worked during a week and x percent more than that rate for hours worked in excess of 40. If the total payroll for the workers at the end of a week in which 40 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 60 hours is $156,800, what is x?

A. 10 percent
B. 20 percent
C. 25 percent
D. 40 percent
E. 50 percent

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Re: A large auto concern that employs 1,000 workers pays each of these wor  [#permalink]

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New post 22 Jan 2018, 08:57
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Bunuel wrote:
A large auto concern that employs 1,000 workers pays each of these workers $4 per hour for the first 40 hours worked during a week and x percent more than that rate for hours worked in excess of 40. If the total payroll for the workers at the end of a week in which 40 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 60 hours is $156,800, what is x?

A. 10 percent
B. 20 percent
C. 25 percent
D. 40 percent
E. 50 percent


As per the question the equation can be written as \(400(4)(20) + 300(40)(4) + 300(40)(4) + 300(20)(40)(1+\frac{x}{100}) = 156,800\)

Solving we get \(x = 20%\)
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Re: A large auto concern that employs 1,000 workers pays each of these wor  [#permalink]

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New post 22 Jan 2018, 05:27
Bunuel wrote:
A large auto concern that employs 1,000 workers pays each of these workers $4 per hour for the first 40 hours worked during a week and x percent more than that rate for hours worked in excess of 40. If the total payroll for the workers at the end of a week in which 40 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 60 hours is $156,800, what is x?

A. 10 percent
B. 20 percent
C. 25 percent
D. 40 percent
E. 50 percent


40 percent of them worked 20 hours
i.e. 400 employees worked for 20 hours each
i.e. their remuneration = $4*20 = $80 each each employee
i.e. Total Remuneration = $80*400 = $32000


30 percent of them worked 40 hours
i.e. 300 employees worked for 40 hours each
i.e. their remuneration = $4*40 = $160 each employee
i.e. Total Remuneration = $160*300 = $48000

Rest 30 percent of them worked 60 hours
i.e. 300 employees worked for 60 hours each
i.e. their remuneration = $4*40+(4+4*x/100)*20 = $160+80+(4x/5) each employee
i.e. Total Remuneration = $[240+(4x/5)]*300 = $72000+240x


Total of all = $32000 +$48000+$72000+240x = $156,800

i.e. x = 20


ANswer: Option B
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Re: A large auto concern that employs 1,000 workers pays each of these wor  [#permalink]

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New post 22 Jan 2018, 08:30
Bunuel wrote:
A large auto concern that employs 1,000 workers pays each of these workers $4 per hour for the first 40 hours worked during a week and x percent more than that rate for hours worked in excess of 40. If the total payroll for the workers at the end of a week in which 40 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 60 hours is $156,800, what is x?

A. 10 percent
B. 20 percent
C. 25 percent
D. 40 percent
E. 50 percent


IMO: B

As per the question
workers hours worked
400 (40%) 20
300 (30%) 40
300 (rest 30%) 60

thus total amount = [400 * 20 * 4] + [300 *40 *4] + {300 [(40 *4) + 20 *(4 + 4x/100)]}
Since for 300 workers who worked for 60 hours, they got 4$ / hour for 40 hours and (4 + 4x/100)$ for next 20 hours

Total amount is given as 156,800$ so we can solve for x

x = 20%

What is the correct answer?
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Re: A large auto concern that employs 1,000 workers pays each of these wor  [#permalink]

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New post 23 Jan 2018, 08:54
Bunuel wrote:
A large auto concern that employs 1,000 workers pays each of these workers $4 per hour for the first 40 hours worked during a week and x percent more than that rate for hours worked in excess of 40. If the total payroll for the workers at the end of a week in which 40 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 60 hours is $156,800, what is x?

A. 10 percent
B. 20 percent
C. 25 percent
D. 40 percent
E. 50 percent


We see that 400 workers worked 20 hours, 300 worked 40 hours and 300 worked 60 hours. We can calculate the total payroll as:

(400 * 4 * 20) + (300 * 4 * 40) + [300 * 4 * 40 + 300 * 4 * 20 * (1 + x/100)] = 156,800

32,000 + 48,000 + 48,000 + 24,000(1 + x/100) = 156,800

128,000 + 24,000 + 240x = 156,800

240x = 4800

x = 20

Answer: B
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Re: A large auto concern that employs 1,000 workers pays each of these wor   [#permalink] 23 Jan 2018, 08:54
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