Chain Rule


Chain rule is also the one of the important topics asked in many interviews, IBPS, PO, bank exam and in many competitive exams. Candidates should understand the concepts before solving the problems. Chain rule is considered as an important topic in all recruitment exams. Perfect time keeping and practicing the aptitude will lead you to success.

LearnFrenzy provides you lots of fully solved "Chain Rule" Questions and Answers with explanation.

Chain Rule Principle

Chain Rule can be applied in questions where two or more than two elements are given. Each element has two figures except one element that has one part missing. Chain rule is used to find out this missing part of an element by subsequent comparison. The other given part of the same element is taken as base and is compared separately with all the other elements e.g. if you have a question having following elements: ‘men’, ‘days’ and ‘hours’. Let us say ‘hours’ are missing then you will compare ‘hours’ with all the other elements independently. Here independently means, comparing ‘hours’ with ‘men’ ignoring the element- ‘days’. Similarly while comparing ‘hours’ and ‘days’ you will ignore the element- ‘men’.

After the comparison, the following two principles are followed:
  1. If the missing part is greater than the given part, then the numerator (N) is kept greater than the denominator (D) i.e. N/D>1, where n & d are the given parts of other element.
  2. If the missing part is smaller than the given part, then the numerator (N) is kept smaller than the denominator (D) i.e. N/D<1, where n & d are the given parts of other element.

Please study the following illustration to understand this concept.

illustration -1: 12 examiners (men) work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would work how many hours per day to check 36000 answer sheets in 36 days?

Answer

Examiners hours answer sheets days
12 16 24000 18
24 ? 36000 36

As we have to calculate the hours in this case, the base would be hours.
Comparisons:

  1. Element = Examiners: If there are 24 examiners now and there were 12 earlier, they need to work lesser hours per day.
  2. Element = Answer sheets: If there are more answer sheets to be checked now, they need to work more hours per day.
  3. Element = Days: If there are more days available, then they need to work lesser hours per day.

Applying chain rule: 16 × (12/24) × (36000/24000) × (18/36) = 6 hours.

In the same illustration if hours were given and answer sheets were missing, then also the method would have been same. Let us solve the same illustration in that manner as well.

illustration - 2: 12 examiners work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would check how many answer sheets working 6 hours a day in 36 days?

Answer

Examiners hours answer sheets days
12 16 24000 18
24 6 ? 36

Following the same steps :
As we have to calculate the answer sheets in this case, the base would be answer sheets.

If there are 24 examiners now and there were 12 earlier, they will check more answer sheets.

If they work for lesser hours per day, they will check lesser answer sheets.
If there are more days available, then they will check more answer sheets.
24000 × (24/12) × (6/16) × (36/18) = 36000.

Chain Rule Formula

  1. Direct Proportion:

    Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

    Eg. Cost is directly proportional to the number of articles.
          (More Articles, More Cost)

  2. Indirect Proportion:

    Two quantities are said to be indirectly proportional, if on the increase of the one, the orther decreases to the same extent and vice-versa.

    Eg. The time taken by a car is covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance.)

    Note: In solving problems by chain rule, we compare every item with the term to be found out.