30 persons working 10 hours a day can do 5 units of work in 12 days. How many people are required to do 8 units of that work in 16 days if they work for 8 hours a day?
- A30
- B38
- C45
- D47
Solution & Step-by-step Explanation
We can use the standard work formula:
W
1
M
1
×D
1
×H
1
=
W
2
M
2
×D
2
×H
2
Where:
M
1
=30 persons
D
1
=12 days
H
1
=10 hours/day
W
1
=5 units of work
M
2
=required number of people
D
2
=16 days
H
2
=8 hours/day
W
2
=8 units of work
Substitute the values into the equation:
5
30×12×10
=
8
M
2
×16×8
Simplifying both sides:
30×12×2=M
2
×16
720=16M
2
M
2
=
16
720
=45
W
1
M
1
×D
1
×H
1
=
W
2
M
2
×D
2
×H
2
Where:
M
1
=30 persons
D
1
=12 days
H
1
=10 hours/day
W
1
=5 units of work
M
2
=required number of people
D
2
=16 days
H
2
=8 hours/day
W
2
=8 units of work
Substitute the values into the equation:
5
30×12×10
=
8
M
2
×16×8
Simplifying both sides:
30×12×2=M
2
×16
720=16M
2
M
2
=
16
720
=45