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A factory that employs 1000 assembly line workers pays each

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A factory that employs 1000 assembly line workers pays each

by swerve » Fri Jun 29, 2018 12:09 pm

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A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 50 hours?

A. $180,000
B. $185,000
C. $190,000
D. $200,000
E. $205,000

The OA is B.

30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*20*5 = 30000

50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000

Remaining 200 worked for 50 Hours

Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000

Total Payment = 30000+100000 + 40000 +15000 = 185000.

Any tip to get this question right, in 2 minutes? It took me 4! Thanks!
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by deloitte247 » Tue Jul 10, 2018 9:55 am
Total number of employees = 1000
Earning $5 per hour for first 40 hours
$$30\%\ \left[\frac{30}{100\ }\ \cdot1000\ =\ 300\right]\ work\ for\ 20\ hours$$
30% wage = 300 * 20 * 5
= $30,000

$$50\%\ \left[\frac{50}{100\ }\ \cdot1000\ =\ 500\right]\ work\ for\ 40\ hours$$
wage for 50% = 500 * 40 * 5
= $100,000
The rest = 100 - [50 + 30]
= 100 - 80
$$=20\%\ =\ \frac{20}{100}\ \cdot\ 1000\ =\ 200$$
200 work for 50 hours = 40 hours at $5 per hour and extra 10 hours at
1.5 * $5 = $7.5 per hour
Wage for 200 - 200 * [40*5 + 10*75]
= 200 * [200 + 75]
=200 * 275
= $55,000
Adding everything together = $100,000
$55,000
$30,000
Total =$185,000
Answer is option B
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by [email protected] » Tue Jul 10, 2018 6:34 pm
Hi swerve,

We're told that a factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. We're asked for the total payroll for the assembly-line workers for a week in which 30 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 50 hours? This question is essentially just about some basic Arithmetic and organized note-taking, but there is a potential 'shortcut' if you recognize that since we're dealing with a multiple of 10 workers, we can calculate the pay for 10 workers under these circumstances - and then multiply that total by 100. There's another minor 'shortcut' if we convert all of the hours into 'standard' hours.

IF.... there were 10 employees, then based on the given percentages...
3 employees would work 20 hours
5 employees would work 40 hours
2 employees would work 50 hours

The first group worked a total of 3(20) = 60 hours
The second group worked a total of 5(40) = 200 hours
The third group worked the equivalent of a total of 2(40) + 2(15) = 110 hours (since each overtime hour is the equivalent of 1.5 standard hours).
Total hours worked = 60 + 200 + 110 = 370 hours
(370 hours)($5/hour) = $1850
Multiplying that total by 100, we would have $185,000

Final Answer: B

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by Shahrukh@mbabreakspace » Tue Jul 10, 2018 11:29 pm
1000*(0.3*20*5+ 0.5*40*5+0.2*40*5+0.2*10*5*1.5)=1000*(30+100+40+15)= 1000*185= 185000
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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:18 pm
swerve wrote:A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 50 hours?

A. $180,000
B. $185,000
C. $190,000
D. $200,000
E. $205,000
So we have 300 workers who worked 20 hours, 500 workers who worked 40 hours, and the remaining 200 workers who worked 50 hours.

For the 300 workers who worked 20 hours, payroll was 300 x (20 x 5) = $30,000.

For the 500 workers who worked 40 hours, payroll was 500 x (40 x 5) = $100,000.

For the 200 workers who worked 50 hours, payroll was 200 x (40 x 5 + 10 x 7.5) = $55,000.

Therefore, the total payroll for all1000 workers is 30,000 + 100,000 + 55,000 = 185,000.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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