Understanding the Concepts of Chain Rule
Chain Rule is a subtopic of Time and Work. The fundamental concept behind the Chain Rule is that a certain number of people will work for a certain number of days to complete the given piece of work.
Generally, work depends upon various parameters like the number of people working, hours per day for which they work, and the number of days for which they operate. In dissimilar group problems, efficiency is also a parameter.
Work done = Number of persons x Time ( Day * Hours )
W = M x T
Here the unit of work is man days or man hours. The problems of time and work can primarily be divided into two types.
The first type includes problems where individuals work with different efficiencies, alone or in combination, to complete a task.
The second type includes problems where group efficiencies are involved. Chain Rule concepts can be applied to group efficiency problems.
Also, when two work scenarios are given, we can change the above formula as,
Example Problem
39 persons can repair a road in 12 days, working 5 hours daily. How many days will 30 people, working 6 hours a day, complete the work?
Applying the chain rule formula, We get
[39(M1)*12(D1)*5(T1)/1(W1)] = [30(M2)*X(D2)*6(T2)/1(W2)]
Here, work is the same in both cases, so we can take it as 1.
39 x 5 x 12 = 30 * X * 6
In conclusion, X = 13 Days.
FAQsFAQs
Why is understanding the concepts of Chain Rule important?
Understanding the concepts of Chain Rule assists in:
Understanding how Chain Rule formulas are derived
Addressing the Chain Rule problems promptly and accurately.
Resolving each of the various forms of questions on the Chain Rule topic
Developing your unique shortcuts
Is it possible to solve Chain Rule problems without knowing the concept?
Yes, it's possible to solve Chain Rule questions without understanding what they entail. However, experts advise that comprehending the fundamentals is essential to address the problems effectively.
What is the right way to learn Chain Rule concepts?
The foundation of mathematics is concepts, and understanding them is critical to boosting your performance in the Quantitative Aptitude section. Visualising the concepts using real-life examples is the best approach to learn the Chain Rule concepts.
