Concept of Net percentage changes and its Application

Net percentage change

There are many situations where we have to deal with percentage changes, these changes are called net percentage changes. We can deal it with a graphic. For example, you have to increase a number 30 by 10 percentage then it can be visualized as
30==10 % increase (3)==>33 [As 10% of 30 is 3]
It is very useful in situations given below

i) Successive changes:

Example 1
A trader gives successive discounts of 10%, 20% and 10% respectively. The percentage of the original cost he will recover is:

Solution:
100==10% decrease (-10)==>90==20% decrease (-18)==>72==10% decrease (-7.2)==>64.8.

Example 2:
A's salary increases by 20% and then decreases by 20%. What is the net percentage change in A's salary?

Solution:
100==20% increase==>120==20% decrease ==>96.
Hence, A's salary has gone down by 4%.

ii) A ==>B ==>A changes:

B's salary is 25% more than A's salary. By what percent is A's salary less than B's salary?

Solution:
100(A)==25% increase ==>125(B)==(-25)==>100(A) A drop of 25 on 125 gives a 20% drop. Hence A's salary is 20% less than B salary.

iii) Product changes:

Let we have a product (10 × 10).
If the first variable changes to 12 and second variables changes to 11, what will be percentage change in the product?

It has to be noticed that first variable 10 changes to 12 that mean 20 % increases and second variable change 10 t0 11 means 10 % increases. Now situation can visualize as,
100==20% increase ==>120==10% increase==>132
Hence, final product shows a 32 % increase.

Similarly, (10*10*10) becomes (11*12*13) then net product's percentage change,
100==30% increase ==>130==20% increase ==>156==10% increase==>171.6.
Hence, the final product got a 71.6 percent increment.
(Since, the product changes from 100 to 171.6).

iv) Final product constant changes:

The price of a commodity has gone up by 25%. In case you required keeping the total expenditure on commodity constant, what percentage you need to cut down the consumption?
100==25 % increase (price effect)==>125==(-25, consumption effect)==>100.
Hence, consumption need to drop by, (25/125)*100= 20%.

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