A workshop employs 6 skilled technicians and 6 apprentices to assemble tractor sub-assemblies. The daily productivity of a skilled technician is $1.5$ times that of an apprentice. The crew completes a full consignment in 12 days. If 2 skilled technicians and 3 apprentices are transferred to another department, the number of days the remaining crew will take to complete an identical consignment is ________ days (answer in integer).
Answer Key:
20
Step-by-Step Solution & Explanation
Let the daily productivity of an apprentice be $1$ unit/day.
Then the daily productivity of a skilled technician is $1.5$ units/day.
1. Initial crew daily work rate:
$R_1 = 6(1.5) + 6(1) = 9 + 6 = 15\text{ units/day}$
2. Total consignment work ($W$):
$W = R_1 \times 12\text{ days} = 15 \times 12 = 180\text{ units}$
3. Remaining crew after transfer:
- Skilled technicians: $6 - 2 = 4$
- Apprentices: $6 - 3 = 3$
New crew daily work rate:
$R_2 = 4(1.5) + 3(1) = 6 + 3 = 9\text{ units/day}$
4. Days required by remaining crew:
$T = \frac{W}{R_2} = \frac{180}{9} = 20\text{ days}$.