Chain Rule

Points to Remember

1) Direct proportion: If the two given quantities (a and b) are so related to each other that if a is multiplied (or divided) by any number, then the other (b) is also multiplied or divided by the same numbers, the quantities are said to be directly proportional to each other.

For example, x's efficiency of work is directly proportional to y's efficiency.

That means if X can complete a work in 2 days, y can also complete that work in 2 days. Similarly, the speed and distance are directly proportional to each other. If the speed of two trains is in the ratio of 1:2, the distance covered by them in the same time would be in the ratio of 1: 2.

2) Inverse proportion: If the two quantities (a, and b) are so related that when "a" is multiplied by any number, then b is required to be divided by the same number, and vice versa, then these quantities are said to be inversely proportional to each other.

For example, Speed and time are inversely proportioned to each other. Let the speed of two trains is in the ratio of 1:2, the time taken by them to cover the same distance would be in the ratio of 2: 1.

3) Chain rule (the rule of three): The method of finding the 4rth term of a proportion when the other three terms are given is called "simple proportion" or "the rule of three" or the "Chain rule."

4) Working rule: Denote the quantity that is to be found as 'x' or 'y' or anything that you want, and set it down as the 4th term.

For example, 5: 15 = 28: x, here x is the quantity that is to be found.

Now, of the three given quantities, set down x (the quantity that is to be found) for the third term, which is of the same kind as the quantity to be found

For example, 5: 15 = 28: x, here 5 and 15 denote work efficiencies, but the 28 denotes days, so the x is also treated as day's quantity that we have to find for a specific condition.