PERCENTAGES
Concept of percentage change
Whenever the value of a measured quantity changes, the change can be captured through
(A) Absolute value change or
(B) Percentage change.
Both these measurements have their own advantages and disadvantages.
Absolute value change : It is the actual change in the measured quantity. For instance, if sales in year 1 is Rs. 2500
crore and the sales in year 2 is Rs. 2600 crore, then the absolute value of the change is Rs. 100 crore.
Percentage change: It is the percentage change got by the formula
Percentage change
As seen earlier, this often gives us a better picture of the effect of the change.
Note: The base used for the sake of percentage change calculations is always the original quantity unless otherwise stated.
Ex .1 The population of a city grew from 20 lakh to 22 lakh. Find the
(A) percentage change
(B) percentage change based on the final value of populaton
Sol. (A) percentage change = (2/ 20) × 100 = 10%
(B) percentage change on the final value
= (2/22) × 100 = 9.09%
Difference between the Percentage Point Change and the Percentage Change
The difference between the percentage point change and the percentage change is best illustrted through an example. Consider this:
This savings rate as a percentage of the GDP was 25% in the first year and 30% in the second year. Assume that there is no change
in the GDP between the two years. Then: Percentage point change in savings rate = 30% – 25% = 5 percentage points.
Percentage change in savings rate
ASSIGNMENT
1. 10% of Mexico’s population migrated to South Asia, 10% of the remaining migrated to America and 10% of the rest
migrated to Australia. If the female population, which was left in Mexico, remained only 3.64,500, find the population of mexico
City before the migration and its effects if it is given that before the migration the female population was half the male population
and this ratio did not change after the migration ?
(A) 10,00,000 (B) 12,00,000 (C) 15,00,000
(D) 16,00,000 (E) 12,50,000
2. Maya has Rs. M with h er and her friend Chanda has Rs. C with Her. Maya spends 12% of her money and Chanda also
spends the same amount as Maya did. What Percentage of her money did Chanda spend ?
(A)18M/C (B) 18C/M
(C)12M/C (D) 12C/M
(E) None of these
3. To pass an examination, 40% marks are essential. A obtains 10% marks less than the pass marks and B obtains 11.11% mark
s less than A. What percent less than the sum of A’s and B’s marks should C obtain to pass the exam ?
(A) 40% (B) 41 (3/17)% (C) 28% (D) Any of these
4. the price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the
cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same ?
(A) 17% (B) 24%
(C) 28% (D) 25%
(E) Cannot be determined
5. Mr. A is a computer programmer. He is assigned three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually).
But due to some technical snag, 10% of the time allotted for each jobs gets wasted. Thereafter, owing to the lack of interset, he invests only 40%,
30%, 20% of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of the total time allotted is the time invested by A ?
(A) 38.33% (B) 39.4545% (C) 32.72% (D) 36.66%
(E) Cannot be determined
6. In the cbse psA Paper, questions were asked in five setions. Out of the total students, 5% candidates cleared the cut-off in all the section and
5% cleared none. Of the rest, 25% cleared only one section and 20% cleared four sections. If 24.5% of the entire candidates cleared two sections
and 300 candidates cleared three sections, find out how many candidates appeared at the cbse psA Paper ?
(A) 1000 (B) 1200
(C) 1500 (D) 2000
(E) 1800
ANSWERKEY
1) C 2) C 3) D 4) A 5) C 6) B