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A senior leader can complete the campaign work in 9 days working 6 hours a day while his supporter can complete same campaign in 12 days working 9 hours a day. In how many days can they complete the campaign work together if they work 8 hours a day? 

A senior leader can complete the campaign work in 9 days working 6 hours a day while his supporter can complete same campaign in 12 days working 9 hours a day. In how many days can they complete the campaign work together if they work 8 hours a day?  Correct Answer 4.5 days

Given:

A senior leader can complete the campaign work in 9 days working 6 hours a day.

The supporter can complete same campaign in 12 days working 9 hours a day.

They together worked for 8 hours a day.

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 senior leader = 1/(9 × 6) = 1/54

⇒ 1 day work of supporter = 1/(12 × 9) = 1/108

1 day work of senior leader and his supporter working 8 hours a day = 8 × = 8 × 1/36 = 1/4.5

Time = Work/Efficiency

⇒ Time taken by senior leader and his supporter to complete work, working 8 hours day = 1/(1/4.5) days = 4.5 days

∴ The work is completed in 4.5 days by senior leader and his supporter when they worked 8 hours day.

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