A and B can complete a certain job in 20 days and 30 days respectively They start the job - Maths - Direct and Inverse Proportions

Question

A and B can complete a certain job in 20 days and
30 days respectively They start the job and work for 3 days Then
B falls sick and unable to work for 5 days during which
A works alone Then again B joins him and they
complete the work together In how many days was the work completed?

Varun.Rawat · Accepted Answer

Number of days taken by A to complete the work alone = 20Number of days taken by B to complete the work alone = 30A's 1 day's work = 120B's 1 day's work = 130A+B's 1 day's work = 120 + 130 = 112A+B's 3 days' work = 312 = 14Now, B falls ill and A works for 5 days alone
A's 5 days' work = 520 = 14Total work done in 8 days = 14+14 = 12amount of work left = 1 - 12 = 12Now, remaining half of the work is completed by both A and B
We know that A and B can complete the work together in 12 daysSo, A and B together can complete half of the work in 6 days
So, total time taken to complete the work = 8 + 6 = 14 days

A and B can complete a certain job in 20 days and 30 days respectively. They start the job and work for 3 days. Then B falls sick and unable to work for 5 days during which A works alone. Then again B joins him and they complete the work together. In how many days was the work completed?