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}}

 

Latest Jobs

  1. Type
    Job Notification
    Job
    IARI Walk-in-Interview for Senior Research Fellows 6th September, 2019
    Location
    DelhiDelhi, India
    Date Posted
    18 Aug 2019
  2. Type
    Job Notification
    Job
    MSDE Recruitment for Chairperson and two Executive Members - August 2019
    Location
    DelhiDelhi, India
    Date Posted
    18 Aug 2019
  3. Type
    Job Notification
    Job
    National Gallery of Modern Art Recruitment - August-2019
    Location
    DelhiDelhi, India
    Date Posted
    18 Aug 2019
  4. Type
    Job Notification
    Job
    Directorate of Lighthouses and Lightships Recruitment Navigational Assistant Grade—III Group-C - 17-08-2019
    Location
    KolkataWest Bengal, India
    Date Posted
    18 Aug 2019
  5. Type
    Job Notification
    Job
    EPIL Recruitment for DGM - Last Date - 07-09-2019
    Location
    DelhiDelhi, India
    Date Posted
    18 Aug 2019
  6. Type
    Job Notification
    Job
    BECIL Recruitment for Junior Engineers 199 - Last Date 21 August 2019
    Location
    DelhiDelhi, India
    Date Posted
    18 Aug 2019
  7. Type
    Job Notification
    Job
    AIIMS Nagpur - Recruitment for Group 'A' Posts on DEPUTATION BASIS - 17-08-2019
    Location
    NagpurMaharashtra, India
    Date Posted
    18 Aug 2019
  8. Type
    Job Notification
    Job
    Indian Pharmacopoeia Commission Recruitment Secretary-cum-Scientific Director - August 2019
    Location
    GhaziabadUttar Pradesh, India
    Date Posted
    13 Aug 2019
  9. Type
    Job Notification
    Job
    CS1R- Central Drug Research Institute Recruitment for Scientist - Last Date 30-09-2019
    Location
    LucknowUttar Pradesh, India
    Date Posted
    13 Aug 2019
  10. Type
    Job Notification
    Job
    Sainik School Satara Maharashtra Recruitment TGT in English - Last Date 04-09-2019
    Location
    SataraMaharashtra, India
    Date Posted
    13 Aug 2019

Jobs by Category

Syllabus and Previous Papers

Leave a Reply

Your email address will not be published. Required fields are marked *