Compound Proportion among three quantities Men, Days, and Time (WP No.1: Compound Proportion)

30 men repair a road in 56 days by working 6 hours daily. In how many days 45 men will repair the same road by working 7 hours daily?

Solution:

 

As the number of Men increases, the days for road repairing will decrease. It is a Inverse proportion. 

As the working time increase, the days for road repairing will  decrease. It is also a Inverse proportion. 

Let the the days for road repairing be ｘ

Here the equation will be 

`\frac{ｘ}{56}`  = `\frac{6}{7}` ｘ `\frac{30}{45}` 

Or

ｘ = `\frac{6}{7}` ｘ `\frac{30}{45}`  ｘ 56 days

by simplifying we get

ｘ =  32 days

Thus, In 32 days, 45 men will repair the same road by working 7 hours daily.

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