A complete a work in 25 days working 8 hours a day.A started the work and worked for one day and next day B joined him who is twice as efficient as A. on next day C is also joined them who is thrice as efficient as A and the process continues.in how many days total work will be get completed if they work 4 hour/day.
Answers
Answer: 5(5/7) days
Step-by-step explanation: See the attached image for solution.
Therefore 9 days 16 hours is needed to complete the total work if everyone worked for 4 hours/week.
Given:
'A' completes work in 25 days working 8 hours a day.
'B' works twice as efficiently as 'A'.
'C' works thrice as efficiently as 'A'.
'A' starts the work, the next day 'B' joins and the next day 'C' joins.
To Find:
Time taken to complete the total work if everyone works for 4 hours/week.
Solution:
The given question can be solved as shown below.
Let us assume that the total work to be done is '200 units'.
Then work done by 'A' per day = 200/25 = 8 units
⇒ And work done by 'A' per hour = 8/8 = 1 unit
⇒ Work done by 'B' per hour = 2 × ( Work done by 'A' ) = 2 units
⇒ Work done by 'C' per hour = 3 × ( Work done by 'A' ) = 3 units
→ Work done by 'A' ( 4 hours ) = 1 unit × 4 = 4 units
→ Work done by 'B' ( 4 hours ) = 2 units × 4 = 8 units
→ Work done by 'C' ( 4 hours ) = 3 units × 4 = 12 units
Total work to be done = 200 units
First day:
Work done by 'A' = 4 units
Second day:
Work done by 'A' and 'B' = 4 + 8 = 12 units
Third day:
work done by 'A', 'B', and 'C' = 4 + 8 + 12 = 24 units
Work done in first 3 days = 4 + 12 + 24 = 40 units
Remaining work to be done = 200 - 40 = 160 units
From the 4th day:
Work done by 'A', 'B', and 'C' = 24 units
Number of days taken to complete remaining work = 160/24 = 6.67 days
Total number of days taken to complete the total work = 3 days + 6.67 days = 9 days 16 hours
Therefore 9 days 16 hours is needed to complete the total work if everyone worked for 4 hours/week.
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