Class 3 : Class 3 Percentages
Profit and Loss
Percentage : Percentage Definition: Per cent means Per hundred or part of hundred. In other words a fraction whose denominator is 100.
Usage: Percentages is used to compare different values which do not have a common base. In other words percentage is a tool for comparison where we use 100 as a common base for comparison.
Percentage : Percentage For calculating percentage we change the base or denominator into 100.
To convert a fraction into percentage we multiply the fraction by 100.
Some fractions that we should memorize as percentages
Fractions. : Fractions. 1/1=100%
1/2 =50%
1/3=33.33%
1/4 =25%
1/5=20%
1/6=16.66% 1/7=14.28%
1/8=12.5%
1/9=11.11%
1/10=10%
1/11=9.09%
1/12=8.33%
Percentage is used : Percentage is used To compare
To measure increase/decrease
Performance Measurement
Ram has got 700 marks out of 800 and shyam has got 725 out of 825 which is better?
Rainfall in delhi last year was 800 cm this year it is 600 cm , what is the percentage decrease?
Slide 6 : Last year, my zonal manager for delhi did a turnover of 15 cr, this year he has managed to do 17.5 cr , I have promised to give him 0.25% of the incremental revenue as incentive, what will be his incentive
Some generalizations : Some generalizations If p1% of the number is x1 and p2% of the number is x2 , then the number would be given by.
x2-x1 X100
p2-p1
If the expenditure on the item is fixed then.. To find the increased or decreased consumption at a particular price
%age change on consumpn=%age change in rate
100+%age change in rate
Generalizations.. contd : Generalizations.. contd If the percentage has changed two times first by x% and then by y% then the total increase/ decrerase in percentage is given by x+y+xy/100.
If there is a product AXB if A changes by x% and B changes by y% then the percentage change in the resultant product will be given by the above fromula only.
Slide 9 : If the two values are respectively x% and y% more than the third value then the first value is( 100+x/100+y)X100 % of the second.
A candidate securing x% marks in an examination fails by a marks and a candidate securing y% marks passes by b marks, then the maximum marks in this examination is given by M=100(a+b)/y-x
If A’s value is x% more than y, then y’s value would be (x/100+x)% less than x.
If A’s value is x% less than y, then y’s value would be (x/100-x)% more than x.
Slide 10 : C.P= cost price
S.P= selling price
S.P-C.P= gain
C.P-S.P= loss.
(S.p-c.p)/C.pX100= gain %
Slide 11 : Question 1 » If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
Question 2 » A shepherd has 1 million sheeps at the beginning of Year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheeps die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheeps. Which of the following is correct?
Question 3 » In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
Slide 12 : Question 4 » A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.
Question 5 » When processing flower-nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?
Question 6 » A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
Slide 13 : Question 7 » If the cost price of 20 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
Question 8 » 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
Question 9 » If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
Question 10 » Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?