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Concept Explained
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This lesson will help you understand the concept of Percentage

Abhishek Khurana
I am Abhishek Khurana. I completed my B.Com(H) from Panjab University in 2008 & my MBA from NMIMS in 2011.

U
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  1. Abhishek Khurana 6 times 99 percentiler in CAT


  2. PERCENTAGES


  3. Introduction *p% p/100 Ex: 25% of 40 -10 30% of 40-12 *percentage change-change as a function of original % increase (final value-initial value/initial value) *100 % decreases(initial value-final value/initial value) *100 *p is what percent more than q? Value by which q is more- q-p/p


  4. Introduction Approaches to solve question: Multiplying factor Approach: Ex1.Amit's salary is 12.5% more than Bharat's. So it is basically 1/8 more than Bharat's. If the base is 8 then 8*1/8-1 8+1-9


  5. Introduction Approaches to solve question: Multiplying factor Approach: Ex2. Santro is 40 % less than alto. Santro*(1-2/5)--Alto (Here 40%-2/5) Santro*3/5 Alto


  6. Introduction Example 1 x is 16.66% more than y, y is how much % less than x?


  7. Introduction Example 1. x is 16.66% more than y, y is how much % less than x? Solution: 1/6 th more. So y*7/6=x y:x 6:7 so % change-7-6/7-14.28%


  8. Introduction Example 2. A number is decreased by 6.25%. By what percentage should the new value be increased to result in original value again?


  9. Introduction Example 2. A number is decreased by 6.25%. By what percentage should the new value be increased to result in original value again? Solution: 6 y4 %--25/400-1/16 Original new 16 so 1/15 6.66% 15(16*(1-1/16))


  10. Introduction Example 3. Length of a rectangle increased by 10% and breadth of rectangle decreases by 20%, % change in arna


  11. Introduction Example 3. Length of a rectangle increased by 10% and breadth of rectangle decreases by 20%, % change in arna Solution: Length 10:11 Breadth 5:4 So area 10*5:11*4 50:44 (50-44/50) *100 6/50 * 100:-12%


  12. Introduction Example 4" Length of a rectangle increases by 10% and The area of the rectangle needs to be increased by 20%The breadth should change by what percent ? Solution: Length 10:11 Area 5:6 Breadth A/L 5/10: 6/11 1/11 * 100-9.09%


  13. Introduction Example 6. Length of a rectangle increases by 10%-Breadth of rectangle decreases by 20%Find the percentage change in perimeter?


  14. Introduction Example 7 . Prices of petrol increased by 12.5%By what percentage should a consumer reduce his consumption so that expenditure is constant. Solution: Price *quantity -expenditure price 8:9 So quantity must be 9:8 so reduction in consumption 1/9 *100 11.11%


  15. Introduction Example 8" Radius of a circle increased by 25%Find percentage change in the area of circle?


  16. Introduction Example 8" Radius of a circle increased by 25%Find percentage change in the area of circle? Solution: Radius 4:5 Area 16:25 so percentage change-9/16 *100-56.25%


  17. Introduction Example 9. My salary increased by 20%"Next year it increased by 25%,what is the total percentage increase over the two years? Solution: Alternative solution: Shortcut: if a quantity increase by p1% and p2 % respectively then net percentage increase pl + p2+ pl*p2/100 20+25+20*25/100 50%


  18. Introduction Example 11. A student instead of increasing a number by 12, decreased the number by 12%.The answer differs from correct answer by what percentage?


  19. Introduction Example 12. Because the price of the petrol is increased by 16.66% I was able to purchase 3 litres less in 126 find the increased price of the petrol(in rs/litre)?


  20. Introduction Example 12. Because the price of the petrol is increased by 16.66% I was able to purchase 3 litres less in 126 find the increased price of the petrol(in rs/litre)? Solution: price 6 7 Quantity x X-3 x/x-3 6/7 so --21 7k*18(21-3) -1260 k-70(increased price)


  21. Introduction Example 13. In a group number of men are 20% more than no of women"62.5% of the men are literate . Of the total literates,33.33% are women . What percentage of women are literate?


  22. Introduction Example 13. In a group number of men are 20% more than no of women.62.5% of the men are literate . Of the total literates,33.33% are women . What percentage of women are literate? Solution: women: men 5:6 40:48 literate(women :men)-15:30 (48*62.5/100-30 so x/30+x-1/3 wherex is the number of literate women) so literate woman= 1540 =37.5 %


  23. Introduction Example 15. Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is


  24. Introduction Example 17. The number of votes not cast for the PNC Party increased by 25% in the National General Election (NGE) as compared to the previous Assembly Polls, and as a result the PNC Party lost In the NGE try a majorlty of twice as many yotes by which it had won the Assembly Polls. If the total of 2,60,000 people voted each time, then how many of them voted for the PNC Party in the previous Assembly Polls? Solution: Total Votes 2,60,000 Let x voters voted against the party in the Assembly Poll. Then votes in favour 260000- Therefore, majority of votes by which party won in previous poll - 260000-x-x = 260000-2x Next year votes against the PNC party increased by 25% So, votes against the party in general election1.25 x And votes polled in favour of the party Total votes - votes against 260000 - 1.25x


  25. Introduction Therefore, majority of votes by which party lost in general election 1.25x- (260000 1.25x) 2.5x - 260000 It is given that, PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls, Therefore 2.5x-260000 = 520000-4X 6.5x 780000 x 1,20,000 Therefore, votes polled by the voters for the party in Assembly Polls for previous year = (2,60,000-x) = (2,60,000-1,20,000) = 1,40,000.


  26. Introduction Example 18, Dipin's score is 15% more than that of Rafi and Rafi's score is 10% less than that of Chandar. If the difference between the scores of Dipin and Chandar is 14, then what is the score of Rafi?


  27. Introduction Example 20. Ravi's present age is 50% of Charu's present age. If a few years ago Ravi's age was 33.33% of the Charu's age, then find out the percentage change in Ravi's age over the time.


  28. Introduction Example 20. Ravi's present age is 50% of Charu's present age. If a few years ago Ravi's age was 33.33% of the Charu's age, then find out the percentage change in Ravi's age over the time. Solution: Suppose Ravi's present age is x Charu's present age 2x Suppose y years ago (2x-y) x 33.33%-(x-y) (2x -y)*1/3 x y 2x-y-3x-3y y years ago, Ravi's age was (x X/2) x/2 Hence, percentage change in Ravi's present age-- (x2/x/2) *100-100%