‘A’ can complete 1/3rd of a work in 4 days. He worked alone for 6 days and left. The remaining work is completed by ‘B’ alone in 10 days. In how many days can ‘A’ and ‘B’ together complete the whole work?

Question: ‘A’ can complete 1/3rd of a work in 4 days. He worked alone for 6 days and left. The remaining work is completed by ‘B’ alone in 10 days. In how many days can ‘A’ and ‘B’ together complete the whole work?

Solution:
A can complete 1/3 of the work in 4 days
A xan complete full work in 12 days
∴ In 6 days A complete 1/2 of work.

∴ B can complete 1/2 of the work in 10 days
∴ B can complete full work in 20 days

∴ In 1 day A and B together can work 1/12 + 1/20 = (5 + 3)/60 = 8/60 = 2/15 of the work

∴ A and B together can complete the full work in 15/2 = 7.5 days