PERCENTAGE

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GETTING STARTED

☛ It is an extension of unitary method only difference being, it is expressed in terms of 100 and not 1.

☛ Per cent means ‘per 100’ and is denoted as %.

Eg. Ramesh scored 88% in his exam and the total marks of the exam was 1200 marks. How much did he score?

Given that Ramesh scored 88% marks it means that if the total marks were 100, he scored 88.

If the total marks were 1200, he would have scored:

88/100 x 1200 = 976 marks

 

☛ For ease of calculations, percentage may have to be converted into decimal fractions and vice versa.

☛ x % is expressed as x/100 and on simplifying we get its corresponding fraction.

Eg. 25% is 25/100 which can be simplified as 1/4

 

☛ Similarly, to express a/b as a percent,we multiply by 100.

Eg. 1/5 in percentage terms is:

      1/5 x 100 = 20%

 

Suppose a boy scored 450 marks out of 600 marks in his exam. Express his marks in percentage.

Soln:. We have to find the marks, person would have obtained out of 100.

450/600 x 100 = 75%

 

☛ If two quantities a and b are multiplied and the product has to remain constant, 

and one of the quantity is increased by y%, then the other quantity has to be decreased by 100y/(100+y) %.

Eg. Ram buys 10 articles worth Rs. 80 each.  How many articles will he buy with the same amount if the price of each item is hiked to Rs. 100 per article.

Soln:. Amount with Ram = No. of articles x Cost per article.

Amount with Ram is a constant. ie. 10 x 80 = Rs. 800

% Increase in price = 20/80 x 100 = 25%

Hence % decrease in no. of articles = (25 x 100/125)% = 20%.

Initially, number of articles = 10.

Decrease of 20 % = decrease of 20/100 x 10 = 2 articles. Therefore, he will be able to buy 8 articles.

 Time speed Distance problems are example for this concept.

☛ Similarly, if a is decreased by x% b will be increased by 100 x/(100-x) %.

 

Appreciation / Depreciation Problems:

☛If a person buys a property for amount A and it appreciates x% per year, the worth after n years,

= A [1+ x/100]n

The value compounds. It is the same method used for finding Compound Interest

 

Similarly, machines depreciate over time

☛ A machine bought for amount A depreciates at x% per year, the worth of machine after n years is :

= A[1-x/100]n

PRACTICE PROBLEMS

1

Percentages - Concept Refresher

1 / 20

In 2010, the market shares of the face creams Clearsil, Glowcare and Chamakdar were 50%, 30% and 20% respectively. Starting from the next year, a new face cream enters the market each year and gets 10% of total market share in that year. The existing soaps in that year share the remaining market in the same ratio as they did in the previous year. What percent of the total market share will Chamakdar have in 2012?

2 / 20

The monthly income of Lakshman increased by 40%. His expenditure which is 60% of his monthly income increased by 50%. His savings must have increased/decreased by

3 / 20

The price of a PC has been decreasing every year by a constant percentage over the last 4 years. If cost of a PC was 100000 4 years ago and it costs Rs.65610 now, find the yearly rate of decrease.

4 / 20

In an election between two candidates P and Q, only 80% of the registered voters cast their vote. Only 70% of the polled votes were valid. P got 55% of the valid votes and won by a margin of 2800 votes. How many registered voters were there?

5 / 20

The breadth of a rectangle decreases by 40% and then increases by 50%. By what percent should the length increase/decrease, so that the area remains unchanged?

6 / 20

Sridhar cut a rectangular piece of paper twice. With the first cut, he decreased its area by 40%. With the second cut, he decreased its area further by 40%. Its final
area was 16 sq cm less than its initial area before first cut. Find its area (in sq cm) after first cut.

7 / 20

The length of a rectangle is increased by 20%. The breadth of the rectangle is increased by 10%. The perimeter of the rectangle increased by x%. The range of x is_____.

8 / 20

In April 2020, Bala spent 75% of his income on food, clothing and entertainment. The amounts that he spent on food, clothing and entertainment is
7 : 6 : 2.
In December 2019, Bala spent 72% of his income on food, clothing and entertainment. The amount that he spent on food, clothing and entertainment is
22 : 19 : 7. The amount he spent on entertainment bills in December 2019 was 16 2/3% more than that in April 2020. The percentage by which his income in December 2019 was less/more than that  of April 2020  is

9 / 20

A new coach was appointed in the middle of a season for Indian cricket team. After he took over, the team won 60% of the 20 matches it played. But the overall success rate of the team was only 40%. Find the minimum number of matches the team must have played that season before the new coach took over.

10 / 20

Mr. Kumar is paid as per the number of hours he puts in per month. The rate of pay was increased by 30% per hour, but the number of hours put in by him went down by 10%. What is the percentage increase/decrease in his income?

11 / 20

Which of the following decimal fractions equal 104 2/5%

12 / 20

32% of what number is 272?

13 / 20

If Ram’s salary is 40% less than Shyam’s salary, by what percentage is Shyam’s salary more than Ram’s salary?

14 / 20

The price of an article is increased by 30%. By what percentage must this price be reduced to bring it down to the original price?

15 / 20

The ratio of the salaries of A and B is 2 : 2 3/5  . By what percentage is B’s salary greater than A’s salary?

16 / 20

42% of a number is 371. Find 78% of that number.

17 / 20

In 2012, Varun’s salary was  Rs.30,000. In 2011, his salary was equal to that of  Ganesh. Ganesh's salary in 2011 was 20% less than his salary in 2012.

Varun’s salary in 2012 was 20% more than his salary in 2011.

By what percentage is the sum of the salaries of  Varun in both the years more / less than that of the Ganesh in both the years?

18 / 20

The price of a Swiss watch was 8000 in 1991. Due to devaluation of the rupee it becomes 9000 in 1992. Find the percentage increase in its price from 1991 to 1992.

19 / 20

The population of a country increased by 20% from 1991 to 1992. It increased by 20% from 1992 to 1993. It increased by 30% from 1993 to
1994. Find the simple average yearly percentage increase in the population from 1991 to 1994.

20 / 20

Rice production in a country increased by 30% from 2005 to 2009. It increased by 20% from 2009 to 2013. Find the percentage increase in the rice production from 2005 to 2013.

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