Examples of Chain Rule 2
In this class, we discuss Examples of Chain Rule 2.
The reader should have prior knowledge of the basics of the chain rule. Click Here.
Example 1:
Suppose the wages of 6 men for 15 days be 2100. then find the wages of 9 men for 12 days.
Solution:
Men increase wages increases – Directly proportional
Days increase wages increase – Directly proportional.
The below diagram shows the presentation of ratios.
The product of extremes = The product of mean terms
6 * 15 * x = 9 * 12 * 2100
x = (9 * 12 * 2100)/(6 * 15)
x = 2520
Example 2:
Fifteen men working 9 hours can reap a field in 16 days.
How many days will 18 men reap the field working 8 hours daily?
Solution:
more men fewer days – indirectly proportional
Fewer hours more days – Indirectly Proportional
The below diagram shows the proportions.
Indirectly proportional, so reverse the ratios.
18 * 8 * x = 15 * 9 * 16
x = 15
Example 3:
A contract was completed in 46 days, and 117 men were set to work, each working 8 hours a day.
4/7 of the work was finished in 33 days.
How many may additional men be employed so that work should be completed in time? Each man is now working 9 hours a day.
Solution:
Remaining work = 1 – 4/7
Remaining days 46 – 33 = 13
less work fewer men – Directly proportional
Fewer days more men – Indirectly proportional
More hours fewer men – Indirectly proportional
The below diagram shows the proportions.
4/7 * 13 * 9 * x = 3/7 * 33 * 8 * 117
x = 198
more men = 198 – 117 = 81