A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
📊 Work and Time Calculation 📊
A does 80% of the work in 20 days.
A’s work rate for the entire work = 100% / (20 days / 0.8)
= 100% / 25 days
= 4% per day
A and B together complete the remaining 20% of the work in 3 days.
Their combined work rate for the remaining work = 20% / 3 days
= 6.67% per day
Since A’s work rate is 4% per day, B’s work rate is:
6.67% – 4% = 2.67% per day
Time taken by B alone to do the whole work = 1 / B’s work rate
= 1 / (2.67/100)
= 100 / 2.67
= 37.5 days
Another method
Let’s assume the total work is 100 units.
A completes 80 units in 20 days, so A’s work rate is 4 units/day.
The remaining 20 units are completed by A and B together in 3 days.
Their combined work rate is 20 units / 3 days = 6.67 units/day.
Since A’s work rate is 4 units/day, B’s work rate is:
6.67 – 4 = 2.67 units/day
Time taken by B alone to do the whole work (100 units) = 100 units / 2.67 units/day
= 37.45 days
🎉 B alone would take approximately 37.45 days to do the whole work. 📊
