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

Answer must clearly be (E)

Any easy approximation method for this?

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

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...

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?

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.

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

Is this question solvable in 2 minutes?

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)