Question)Tina can do as much work in 2 days as Leena can do in 3 days and Leena can do as much work in 4 days as Meena can do in 5 days. If all three work together, they take 20 days to finish a work. How long would Leena take to finish the work if she works alone?
Solution: Work by Tina in 2 days = Work by Leena in 3 days
Work by Leena in 4 days = Work by Meena in 5 days
Combining: Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days
Let the work be the LCM (least common multiple) of 8, 12, 15 = 120 units
=> Work by Tina in 8 days = Work by Leena in 12 days = Work by Meena in 15 days = 120 units
=> Work by Tina in 1 day = 15 units; Work by Leena in 1 day = 10 units; Work by Meena in 1 day = 8 units
=> Work done by all three together in 1 day = 33 units
=> Work done by all three together in 20 days (total work duration) = 660 units
Thus, total work volume is of 660 units
=> Time taken by Leena to complete the work = 660/10 = 66 days
Answer C
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