Amrita, working alone, can accomplish her sales target in 15 days, while Varshita, working alone, takes ____ days to complete her sales target. If they collaborate, Amrita and Varshita together can achieve the same target in ___ days. Which set of values from the following options fills the blanks in the same order, making the statement true?
I. 10, 6
II. 11, 6.75
III. 12, (20/3)

ATQ, Let total target = L.C.M of 15 and 10 = 30 units So, efficiency of ‘Amrita’ alone = (30/15) = 2 units/day Efficiency of ‘varshita’ alone = (30/10) = 3 units/day So, time taken by ‘Amrita’ and ‘varshita’ together to complete the target= 30 ÷ (2 + 3) = 6 days So, I is true. From II: Let total target = L.C.M of 15 and 11 = 165 units So, efficiency of ‘Amrita’ alone = 165 ÷ 15 = 11 units/day Efficiency of ‘varshita’ alone = 165 ÷ 11 = 15 units/day So, time taken by ‘Amrita’ and ‘varshita’ together to complete the work = 165 ÷ (11 + 15) ~ 6.34 days ≠ 6.75 days So, II is not true. From III: Let total target= L.C.M of 15 and 12 = 60 units Efficiency of ‘Amrita’ alone = 60 ÷ 15 = 4 units/day Efficiency of ‘varshita’ alone = 60 ÷ 12 = 5 units/day So, time taken by ‘Amrita’ and ‘varshita’ together to achieve sales target is = 60 ÷ (4 + 5) = (20/3) days So, III is true.