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?
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Answer is :- 12 days
Step-by-step explanation:
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.
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