At a construction site, 15 men or 10 machines can construct a room in 66 days. In how many days can 5 men and 4 machines together complete the work?
- A80
- B75
- C85
- D90
Solution & Step-by-step Explanation
Given that the work done by 15 men is equal to the work done by 10 machines:
15 Men=10 Machines
1 Men=
15
10
Machines=
3
2
Machines
Total work in terms of machines can be given as:
Total Work=10 machines×66 days=660 machine-days
Now, we need to find the work done by 5 men and 4 machines together. Convert men into machines:
5 men+4 machines=5×(
3
2
) machines+4 machines
=
3
10
+4=
3
22
machines
Let D be the number of days required by them to finish the work:
3
22
×D=660
D=
22
660×3
D=30×3=90 days
15 Men=10 Machines
1 Men=
15
10
Machines=
3
2
Machines
Total work in terms of machines can be given as:
Total Work=10 machines×66 days=660 machine-days
Now, we need to find the work done by 5 men and 4 machines together. Convert men into machines:
5 men+4 machines=5×(
3
2
) machines+4 machines
=
3
10
+4=
3
22
machines
Let D be the number of days required by them to finish the work:
3
22
×D=660
D=
22
660×3
D=30×3=90 days