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F alone can complete a work in 24 days and G alone can complete the same work in 32 days. F and G start the work together but G leaves the work 8 days before the completion of work. In how many days the total work will be completed? 

F alone can complete a work in 24 days and G alone can complete the same work in 32 days. F and G start the work together but G leaves the work 8 days before the completion of work. In how many days the total work will be completed?  Correct Answer 120/7 days

Given:

Time taken by F alone = 24 days

Time is taken by G alone = 32 days

G leaves the work 8 days before the completion of work

Formula Used:

Total work = Time taken × Efficiency

Calculation:

Let the total work be LCM of 24 and 32 i.e. 96 unit

Work done by F in 1 day = 96/24 = 4 unit

Work done by G in 1 day = 96/32 = 3 unit

G leaves the work 8 days before the completion of work, so F worked alone for 8 days

Work done by F in 8 days = 4 × 8 = 32 unit

Work left = 96 - 32 = 64 unit

64 unit work is done by both G and F

Time taken to complete 64 unit work = 64/(4 + 3) = 64/7 days

∴ Total time taken = 8 days + 64/7 days = 120/7 days

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