Concept of Base
x as a percentage of y = 𝑥/𝑦 × 100%
Here, y is the base.
E.g. Mragank scores 60% marks. - So here maximum marks is the base
As percentage is given, the absolute marks obtained by Mragank will vary as base changes.
60% marks, if maximum marks are 100 = 60
60% marks, if maximum marks are 120 = 72
E.g. Mragank scores 60 marks. - x is given
As absolute marks obtained by Mragank are given, percentage will vary as base changes.
Percentage of 60 marks, if maximum marks are 100 = 60%
Percentage of 60 marks, if maximum marks are 120 = 50%
Q. Country A spends 2% and 3% of its GDP on health and education respectively. While country B spends 3% and 4% of its GDP on health and education respectively.
(a) Expenditure on health by country A is less than the expenditure on health by country B
(b) Expenditure on health by country A is more than the expenditure on health by country B
(c) Expenditure on education by country A is less than the expenditure on education by country B
(d) Country B spends more on education than on health.
However, we can compare the percentage values of the same country as the base will be the same.
So, if total GDP of country B = y
Then, 4% of y > 3% of y
Q. In a trade fair, exactly 20.25% of the visitors visited the books section. What must be the minimum number of people who must have visited the trade fair?
(a) 100 (b) 400 (c) 200 (d) 800
Here we have to find the base, such that the final result is an integer.
Let the number of people who visited the trade fair be x.
Now, the number of people (i.e. x) must be a natural number. Also, the number of visitors that visited the books section (i.e. 20.25% of x) must be a natural number too.
20.25% of x = (20.25/100) × x = (81/400) × x
(81/400) × x must be an integer, so x must be a multiple of 400.
Hence, the minimum value that x may attain = 400.
20.25% of x must be a natural number. Hence, 0.25% of x must be a natural number too.
Minimum possible value of x that allows it is x = 400. (then 0.25% of 400 = 1, i.e. the least possible natural number).