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Question

A can finish finish the work in 16 days and B can finish a piece of work in 12 days a started the work and work at it for 2 days he was then joined by b find the total number of time taken to finish the work

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Solution

A finishes the work in 16 days.

A finishes 1/16 of the work in one day.

A had worked for two days= 2*1/16 = 1/8

the work left after A has worked for two days = 1- 1/8 = 7/8

B finihses the work in 12 days

in 1 day B finishes 1/12 of the work.

A and B togeher in one day can finish= 1/16+1/12 = (3+4)/48= 7/48 of work

A and B together can complete the remaining work= (7/8) / (7/48)= 7*48/8*7 = 6 days.

therefore total time taken = 2 days by A alone + 6 days by both Aand B = 8 days


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