Question
'Zara' is capable of finishing a specific task in 60
days. On the other hand, 'Armaan' takes 40% more time than 'Zara' to complete the same task, while 'Tara' takes 75% more time than 'Zara.' 'Armaan' began the work but received assistance from 'Tara' and 'Zara' every third day. Your task is to determine the total time required to complete the entire task. (Calculate approximate value )Solution
ATQ, Time taken by ‘Armaan’ alone to complete the whole task= 1.40 × 60 = 84 days Time taken by ‘Tara’ alone to complete the whole task = 1.75 × 60 = 105 days Total task = 420 units (LCM of 60, 84 and 105) Efficiency of ‘Armaan’ = 420/84 = 5 units per day Efficiency of ‘Tara’ = 420/105 = 4 units per day Efficiency of ‘Zara’ = 420/60 = 7 units per day Task completed by ‘Armaan’, ‘Tara’ and ‘Zara’ together in 3 days = 5 + 5 + 16 = 26 units Task done by Armaan, Tara and Zara together in 48 days = 16 × 26 = 416 units Remaining 4 units Task will be completed by Armaan alone in 4/5 days Hence required time = 48 + (4/5) = 48.8 days or 49 days
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