Question

A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?

Answer 1

we know that,

Number of days A required to do piece of work = 14 days

Number of days B required to do piece of work = 21 days

∴ We can calculate, work done by A in 1 day = 1/14

Work done by B in 1 day = 1/21

Work done by A, B together in a one day = 1/14 + 1/21 = 5/42

∴ they can work together in 42/5 days.

A and B work for 6 days and the work completed by A and B in 6 days = 6 × 5/42 = 5/7

∴ work left = 1- 5/7 = 2/7

Number of days taken by B to complete the left over work = 2/7 × 21 = 6 (21 is used because 21 is the days required by B to complete a piece of work)

Time taken to complete the work = 6 + 6 = 12days

∴ Total time taken to complete the work =12days.