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Question

Six men working 10 hours a day can do a piece of work in 24 days. In how many days will 9 men working for 8 hours a day do the same work?

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Solution

Method 1: The problem involves 3 sets of variables, namely - Number of men, Working hours per day and Number of days.
Number of MenNumber of hours per dayNumber of days
6 10 24
9 8 x
Step 1: Consider the number of men and the number of days. As the number of men increases from 6 to 9, the number of days decreases. So it is in Inverse Variation.
Therefore the proportion is 9:6::24:x .....(1)
Step 2: Consider the number of hours worked per day and the number of days. As the number of hours working per day decreases from 10 to 8, the number of days increases. So it is inverse variation.
Therefore the proportion is 8:10::24:x .....(2)
Combining (1) and (2), we can write as
9:68:10::24:x
We know, Product of extremes = Product of Means.
ExtremesMeansExtremes9:6::24:x8:10
So, 9×8×x=6×10×24
x=6×10×249×8=20 days
Method 2: (Using arrow marks)
Number of MenNumber of hours per dayNumber of days
6 10 24
9 8 x
Step 1: Consider men and days. As the number of men increases from 6 to 9, the number of days decreases. It is in inverse variation.
The multiplying factor =69
Step 2: Consider the number of hours per day and the number of days. As the number of hours per day decreases from 10 to 8, the number of days increases. It is also in inverse variation.
The multiplying factor =108
x=69×108×24=20 days.

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