A and B working together can complete a job in 30 days. The ratio of their efficiencies is 3:2. In how many days can the faster person complete the job?
- A50
- B30
- C40
- D60
Solution & Step-by-step Explanation
Let the efficiencies of A and B be 3x and 2x units/day respectively.
The faster person is A with an efficiency of 3x.
Combined efficiency of A and B:
Total Efficiency=3x+2x=5x units/day
Total work to be completed:
Total Work=Combined Efficiency×Time=5x×30=150x units
Time taken by the faster person (A) to complete the job alone:
Time=
Efficiency of A
Total Work
=
3x
150x
=50 days
The faster person is A with an efficiency of 3x.
Combined efficiency of A and B:
Total Efficiency=3x+2x=5x units/day
Total work to be completed:
Total Work=Combined Efficiency×Time=5x×30=150x units
Time taken by the faster person (A) to complete the job alone:
Time=
Efficiency of A
Total Work
=
3x
150x
=50 days