A can do a certain job in 12 days. B is 60% more efficient than A. To do the same job B alone would take:
- A7 \frac{1}{2} days
- B8 days
- C10 days
- D7 days
Solution & Step-by-step Explanation
1. Establish the ratio of efficiencies:
Let the efficiency of A be 100%.
Since B is 60% more efficient than A, B's efficiency is 100%+60%=160%.
Efficiency of B
Efficiency of A
=
160
100
=
8
5
Use the inverse relationship between efficiency and time:
Efficiency×Time=Total Work
Efficiency of A×Time of A=Efficiency of B×Time of B
5×12=8×Time of B
60=8×Time of B
Time of B=
8
60
=
2
15
=7
2
1
days
Thus, B alone takes 7
2
1
days.
Let the efficiency of A be 100%.
Since B is 60% more efficient than A, B's efficiency is 100%+60%=160%.
Efficiency of B
Efficiency of A
=
160
100
=
8
5
Use the inverse relationship between efficiency and time:
Efficiency×Time=Total Work
Efficiency of A×Time of A=Efficiency of B×Time of B
5×12=8×Time of B
60=8×Time of B
Time of B=
8
60
=
2
15
=7
2
1
days
Thus, B alone takes 7
2
1
days.