Chain Rule - Important Formulas, Questions and Study Material

Chain Rule Important Questions - Page 3
Chain Rule Video Lecture - Page 4

When quantities of different kinds are connected to one another so that we know how much of one quantity is equivalent to a given quantity of a second, etc. We can determine how much of the last kind is equivalent to a given of first kind by the chain rule.

Proportion and Indirect Proportion

If increase or decrease of a quantity Q_{1} causes increase or decrease of another quantity Q_{2} in the same extent then, Q_{1} is directly proportional to Q_{2}\Rightarrow Q_{1}\propto Q_{2}

1) Number of persons \propto Amount of work done, i.e. more persons, more work

2) Number of days \propto Amount of work, i.e. more days, more work

3) Working rate \propto Amount of work, i.e. more working rate, more work

4) Efficiency of man \propto Amount of work, i.e. more efficiency of man, more work
Combining I,II,III,and IV, (Man\times Days\times Work \,rate\times Efficiency) \propto Amount of work. If increase of a quantity  Q_{1} is\, indirectly \,proportional\, to \,Q_{2}\Rightarrow Q_{1}\propto \frac{1}{Q_{2}}

5) Number of men \propto\frac{1} {No.\,of \,days}, i.e. more the men, less the no. of days required

Chain Rule Important Formulas

1)  \frac{Man_{1}\times Days_{1}\times Work\, rate_{1}}{Amount \,of\, work\,done_{1}}=\frac{Man_{2}\times Days_{2}\times Work\,rate_{2}}{Amount \,of \,work\,done_{2}}

Remember, “Man days” required per unit work is always same. In fact,  Man \times Days specify the volume of job or work.

2) If in place of men there are engines burning coal for certain number of hours, then, the above equation changes to

 \frac{Number\, of \,engine_{1}\times Hours_{1}\times Consumption \,Rate_{1}}{Amount\, of\, coal \,burnt_{1}}=\frac{Engine_{2}\times Hours_{2}\times Consumption \,Rate_{2}}{Amount\, of\, coal\, burnt_{2}}

Because, here the job of engine is to burn the coal.

3) If number of examiners examining a number of answer books in number of days by working a number of hours or day, since the job of examiner is to check the answer books,

then,  \frac{Number\, of\, examiner_{1}\times Days_{1}\times Work\, Rate_{1}}{No.\,of \,answer\, books checked_{1}}=\frac{Examiner_{2}\times Days_{2}\times Work\, Rate_{2}}{No.\,of\, answer\, books\, checked_{2}}


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