Direct & Inverse Relation - Part 1 (Intro)

We all know direct/inverse proportion very well

If x varies directly with y …
…. when x increases, y also increases and when x decreases, y also decreases.

This is a very layman-ish understanding but will serve our purpose. However in the above, a very important aspect is missed out! That of a proportional increase or decrease. So if x increases, y increases proportionally i.e. if x doubles, y will also double and if x becomes one-third, y will also become one-third.

Now consider the following question:

Q. 1: When 20 people go on a picnic, the cost is Rs. 3750 and when 40 people go on a picnic, the cost is Rs. 6250. What is the cost of the picnic, if 50 people go on the picnic?

The number of people has increased from 20 to 40 i.e. doubled.
Has the cost increased? Yes it has.
Has the cost increased proportionally i.e. has it doubled? No.

Thus, there is a ‘direct relation’ but not ‘direct proportion’.

This happens because: The cost of the picnic is partly constant and partly varies directly with the number of people.

Thus, the part that varies directly with number of people would have increased, in fact would have doubled. But the part that is constant would remain the same. Hence the total cost does increase, but not proportionally.

Now your task is to solve the question. That is not a big deal, if you are applying pencil to paper and solving it through equations. You have to devise a very logical and oral way to solve such situations of direct relation. Solution and further interesting twist tomo.

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