Bunuel wrote:
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
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)
=
$178500Correct choice -> E Best Regards,
Ashish Arora
Quant Expert,
e-GMAT _________________