A factory that employs 1,000 assembly-line workers pays each of these

Question

A factory that employs 1,000 assembly-line workers pays each of these workers $6 per hour for the first 35 hours worked during a week and 1.25 times that rate for hours worked in excess of 35. What was the total payroll for the assembly line workers for a week in which 60 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 50 hours?

A. $150,500
B. $155,000
C. $ 162,500
D. $168,000
E. $178,500

A. $150,500
B. $155,000
C. $ 162,500
D. $168,000
E. $178,500

adstudy · Accepted Answer

Kritisood I think an easier, or rather faster, way to solve this problem would be to comprehend it the following way - 1. 600 Employees -> $6 per hour -> 20Hours each => 600 x 6 x 20 = $72000 2. Remaining 400 Employees --> $6 per hour -> 35Hours each and, --> $7.5 per hour -> 5 Hours each => 400 x 6 x 35 = (35x2) x 1200 = 70 x 1200 = $84000 => 400 x 7.5 x 5 = (7.5x2) x (5x200) = 15 x 1000 = $15000 The highlighted part is a total of $171000 and we are still left with one more case to be added to these values. Hence answer automatically turns out to be E Hope this helps in reducing the time for you. With this I was able to solve in just about 2 minutes.

Bambi2021 · Answer

Number of hours to pay 6$ = 600*20 + 300*35 + 100*35 = 12000 + 400*35 = 12000 + 14000 = 26 000

6*26000 = 156 000

Number of hours to pay 7,5$ = 300*5 + 100*15 = 1500 + 1500 = 3000

3000*7,5 = 22500

156000 + 22500 = 178500

Abhishek009 · Answer

Capture.PNG Answer must clearly be (E)

apati10 · Answer

Any easy approximation method for this?

Posted from my mobile device

Kritisood · Answer

any easy way to calculate this? Avg time taken is 4 mins for this ques..

CEdward · Answer

Took 5 minutes at an snail's pace. It was clear from the get-go what the question wants, but some of the calculations were a drag...

ueh55406 · Answer

QQ

1.25 times that rate for hours worked in excess of 35   << How are we getting this rate? I understand we just broke 40 into 35 (for which we have 6 $/hr) and 5 hours for which rate needs to be 1.25 time the rate. so how do we get 7.5 for the rest 5 hours?

SSM700plus · Answer

This is really quicker ways to solve. Just calculate total no. of hours to be paid that is ( No. of hours <= 35) and (No. of hours to pay >= 35).
And then multiply with the cost.

It works because we are doing all simple calculation together and therefore reducing overall time to solve problem.

egmat · Answer

GIVEN:

Total number of employees = 1000 
 Rate:  $6 per hour for first 35 hours; 1.25 times of $6 (1.25 × 6 =  $7.5 ) per hour for every hour beyond the first 35 hours. 
 60% of employees worked for 20 hours ,  30% worked 40 hours  and the  rest (10%) worked for 50 hours in a week.

Let’s assign BATCH – 1 to the 60% who worked for 20 hours, 
BATCH – 2 to the 30% who worked for 40 hours, 
BATCH – 3 to the 10% who worked for 50 hours,

TO FIND: 
  
Total payroll for the assembly line workers for the week

SOLUTION:

Strategy : To make calculations faster, we will first calculate the number of employee hours for which the rate would be $6, then the number of employee hours for which the rate would be $7.5, and then perform the multiplication at last. (You can try multiplying for each case to see why I chose my way. 😊)

Total #hours worked by BATCH - 1

No of employees in batch – 1 = 60% of 1000 =  600  
  Each employee worked for 20 hours at $6/hour (Since 20 < 35)  
 Hence, 600 employees worked for 600 * 20 =   12000 hours   at $6/hour.   
 
 Total #hours worked by BATCH - 2

No of employees in batch – 2 = 30% of 1000 =  300  
  Each employee worked for 40 hours => 
  35 hours at $6/hour and 5 hours at $7.5/hour. (Since 40 – 35 = 5)    
 Hence, 300 employees worked for: 
  300 * 35 =  10500 hours  at $6/hour AND  
 300 * 5 =  1500 hours  at $7.5/hour.

Total #hours worked by BATCH - 3 
 
No of employees in batch - 3 = 10% of 1000 =  100 
  Each employee worked for 50 hours => 
  35 hours at $6/hour and 15 hours at $7.5/hour. (Since 50 – 35 = 15)    
 Hence, 100 employees worked for: 
  100 * 35 = 3500 hours at $6/hour AND  
 100 * 15 = 1500 hours at $7.5/hour.

CALCULATING PAYROLL

Total employee hours at $6 = 12000 + 10500 + 3500 =  26000 hours  
Total employee hours at $7.5 = 1500 + 1500 =  3000 hours

Thus,  total payroll = $6 * 26000 + $7.5 * 3000  
 =  $156000 + $22500  (To make the calculation faster first multiply 7 with 3000 and then add it to 0.5 times 3000) 
 = $178500

Correct choice -> E

Best Regards,

Ashish Arora 
Quant Expert, e-GMAT

Vikasgarg1 · Answer

Is this question solvable in 2 minutes?

joaoalencar023 · Answer

If you do the math by total hours worked:

- 60% worked 20h => 600*20= 12.000
- 30% worked 40h => 300*40= 12.000
- 10% worked 50h => 100*50= 5.000

Total Hours Worked: 29.000

If the rate for all the Hours was $6, the total would be 174.000. Hence, we can safely assum $ 178.500 is the right answer.

(E)

Kavicogsci · Answer

Bunuel   KarishmaB  is there a faster way to solve this?
One way that people said is to cal the total hrs and multiply by 6 and as that ans is v close to the highest answer option we can assume...but in case there were two such choices...any better way to approach this problem?

KarishmaB · Answer

Assume there are 10 workers instead of 1000 to deal with smaller numbers. We will multiply the result by 100 later on. Hence 60% of workers are 6 workers, 30% are 3 workers and rest are 1 worker.

For all hours, $6 is certainly paid so that needs to be added up = (6 * 20 + 3 * 40 + 1 * 50)* $6
For extra hours after 35, another 25% of 6 that is extra $1.5 is paid = (3 * 5 + 1*15) * $1.5

Hence, (6 * 20 + 3 * 40 + 1 * 50)* $6 + (3 * 5 + 1*15) * $1.5 = $1785

Multiply back by 100 to get $178500

Answer (E)

Ngocanhvy · Answer

It's better to seperate into 2 calculation: 6$/hour, and 7.5$/hour (7.5 = 1.2*6)
60%, 30%, the rest of total workers is: 600. 300,100 respectively

Total payroll of 6$/hour = (600*20 + (100+300)*35)*6 = (600*20 + 400*35)*6 = (6*2 + 4*35)*6*100 = (120 + 140)*6*100 = 260*6*100 = 26*6*1000 = 156,000

Total payroll of 7.5$/hour = ((300*(40-35) + 100*(50-35)) * 7.5 = (300*5 + 100*15)*7.5 = (3*5 + 15)*7.5*100 = 30*7.5*100 = 75*3*100 = 22,500

Total payroll: 156,000 + 22,500 = 178,500

A factory that employs 1,000 assembly-line workers pays each of these

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A factory that employs 1,000 assembly-line workers pays each of these

Prep Toolkit

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