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4 junior labourers can complete the house in 60 days while 8 senior labourers can complete same house in 20 days. In how many days can 6 junior and 4 senior labourers complete the house if they work together? 

4 junior labourers can complete the house in 60 days while 8 senior labourers can complete same house in 20 days. In how many days can 6 junior and 4 senior labourers complete the house if they work together?  Correct Answer 20 days

Given:

4 junior labourers can complete the house in 60 days.

8 senior labourers can complete same house in 20 days.

Concepts used:

1 day work done by individual = Work/time

Time = Work/Efficiency

Calculation:

1 day work done by individual = Work/time

1 day work of 1 junior labourer = 1/(4 × 60) = 1/240

⇒ 1 day work of 6 junior labourers = 6/240 = 1/40

1 day work of 1 senior labourer = 1/(8 × 20) = 1/160

⇒ 1 day work of 4 senior labourers = 4/160 = 1/40

⇒ 1 day work of 6 junior and 4 senior labourers together = (1/40) + (1/40) = 1/20

Time = Work/Efficiency

⇒ Time taken by 6 junior and 4 senior labourers to complete work together = 1/(1/20) days = 20 days

∴ 6 junior and 4 senior labourers can complete the house in 20 days. 

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