Question

Parikh explained a project that he intends to build for credit in his course on image processing, to Navdeep. He further explained that he alone can complete it in 80 days. Navdeep admitted that it would take 120 days for him to complete it alone. So, they both started to complete the project. However, Parikh left it after 20 days and Navdeep kept working on it alone. Navdeep worked alone for 12 days and then Rohan offered to help. Rohan and Navdeep worked hand-in-hand and completed the project in 34 more days. Given the scenario, can you tell us how many days it would have taken Rohan to complete the project alone.

Answer 1

Solution :-

→ LCM of 80 and 120 = 240 units = Let total work .

so,

→ Efficiency of Parikh = Total work / Total days = 240/80 = 3 units / day .

and,

→ Efficiency of Navdeep = Total work / Total days = 240/120 = 2 units / day .

so,

→ In first 20 days both navdeep and parikh completed = (3 + 2) * 20 = 100 units .

and,

→ In next 12 days navdeep alone completed = 12 * 2 = 24 units .

then,

→ Left work to be done = 240 - (100 + 24) = 116 units .

now, let us assume that, efficiency of Rohan is x units / day .

therefore,

→ 34(Navdeep + Rohan) = 116 units .

→ 34(2 + x) = 116

→ 68 + 34x = 116

→ 34x = 116 - 68

→ 34x = 48

→ x = (48/34) = (24/17) units .

hence,

→ Time taken by Rohan alone to complete the work = Total work / Efficiency = 240/(24/17) = 240 * (17/24) = 170 days (Ans.)

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Answer 2

Answer: 112 days

Step-by-step explanation:

Total Number of days Parikh worked = 20 days

Total Number of days Navdeep worked = 60 days (20+12+28)

Total Number of days Rohan worked = 28 days

Let x be the number of days Rohan takes to complete the project alone. 20/80 + 60/120 +28/x = 1

28/x= 1 - 1/2 -1/4

28/x = 1/4

x= 112 days