A machine can complete double the work that a man can complete in a given period of time. To complete a work, 10 machines and 5 men take 60 days. If there were 10 men and 5 machines, then the time it would have taken to complete the work is:
- A90 days
- B84 days
- C68 days
- D75 days
Solution & Step-by-step Explanation
Let the efficiency of a man be M and the efficiency of a machine be M
c
.
Given that a machine does double the work of a man in the same time:
M
c
=2M
Case 1: 10 machines and 5 men take 60 days.
Total efficiency=10M
c
+5M=10(2M)+5M=20M+5M=25M
Total Work=Total efficiency×Days=25M×60=1500M
Case 2: Find the time taken (D) by 10 men and 5 machines to complete the same work.
New efficiency=10M+5M
c
=10M+5(2M)=10M+10M=20M
Time taken (D)=
New efficiency
Total Work
=
20M
1500M
=75 days
c
.
Given that a machine does double the work of a man in the same time:
M
c
=2M
Case 1: 10 machines and 5 men take 60 days.
Total efficiency=10M
c
+5M=10(2M)+5M=20M+5M=25M
Total Work=Total efficiency×Days=25M×60=1500M
Case 2: Find the time taken (D) by 10 men and 5 machines to complete the same work.
New efficiency=10M+5M
c
=10M+5(2M)=10M+10M=20M
Time taken (D)=
New efficiency
Total Work
=
20M
1500M
=75 days