1.

A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the work.

Answer»

we know that,

Number of days A required to do piece of work = 16 days

Number of days B required to do piece of work = 12 days

∴ We can calculate, work done by A in 1 day = 1/16

Work done by B in 1 day = 1/12

A alone works for 2 days and the work completed by A in 2 days = 2 × 1/16 = 1/8

∴ work left = 1- 1/8 = 7/8

Work done by A, B together in a one day = 1/16 + 1/12 = 7/48

∴ they can work together in 48/7 days

But 7/8th work is completed by both A and B

∴ time required to complete 7/8th work together by A and B = 7/8 × 48/7 = 6 days

Time taken to finish the work = 6 + 2 = 8 days(2 is added because 1/8 work is done by A alone)

∴ Total time taken to complete the work = 8 days.



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