Question
Person A and Person B can complete the work alone in 18 days and 24 days, respectively, and the efficiency of Person C is -----% greater than the efficiency of Person A. If Person B starts the work and after 3 days, Persons A and C join in, then the entire work is finished in ---- days. Which of the following options will fit into the blanks provided in the question?
- A 10%, 6.4 days
- B 15%, 5.2 days
- C 20%, 8.3 days
Solution
Answer: D From (A): C = 100/110 * 18 = 180/11 (x + 3)/24 + x/18 + 11x/180 = 1 7.5x + 22.5 + 10x + 11x = 180 28.5x = 157.5 x = 5.5 Required time = 3 + 5.5 = 8.5 days This does not satisfy. From (B): C = 100/115 * 18 = 360/23 (x + 3)/24 + x/18 + 23x/360 = 1 15x + 45 + 20x + 23x = 360 x = 315/58 = 5(25/58) Required time = 3 + 5(25/58) days = 8(25/58) days This does not satisfy. From (C): C = 100/120 * 18 = 15 (x + 3)/24 + x/18 + x/15 = 1 7.5x + 22.5 + 10x + 12x = 180 x = 157.5/29.5 5.3 Required time = 3 + 5.3 = 8.3 days This satisfies.
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