Question

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?

• A. 130/5 days
• B. 106/7 days
• C. 114/7 days
• D. 120/7 days

Answer 1

Answer:

D. 120/7 days

Solution: 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