A can do 2/5 of a work in 10 days. B can do 1/2 of the same work in 10 days. They worked together for 5 days and then A left. In how many days will B finish the remaining work?

Correct option is C

A’s work rate: If A finishes $$\tfrac{2}{5}$$​​ of the job in 10 days, then A does$$\frac{2/5}{10} = \frac{1}{25}$$​​ of the job per day. Thus, A alone can complete the entire job in 25 days.
B’s work rate: If B finishes $$\tfrac{1}{2}$$​​ of the job in 10 days, then B does $$\frac{1/2}{10} = \frac{1}{20}$$​​ of the job per day. B alone can complete the entire job in 20 days.
Together for 5 days: Their combined daily rate is $$\frac{1}{25} + \frac{1}{20} = \frac{4}{100} + \frac{5}{100} = \frac{9}{100}.$$​
In 5 days, they complete $$\tfrac{9}{100} \times 5 = \tfrac{45}{100} = \tfrac{9}{20}.$$​
Remaining work: $$1 - \tfrac{9}{20} = \tfrac{11}{20}​.$$​
B alone finishes: $$\tfrac{11}{20}​$$​ divided by B’s rate $$(\tfrac{1}{20}​)$$​ is $$\tfrac{11}{20} \div \tfrac{1}{20} = 11$$​