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