Banks and SSC - Percentages
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This document provides information on percentages and percentage calculations. It includes sections on the relationship between percentages and fractions, percentage change calculations, successive increases and decreases, product constancy, and partnerships. Examples of percentage problems are provided throughout with step-by-step explanations. The document is intended as a study guide for bank exams and other competitive exams that include questions on percentages.
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Banks and SSC - Percentages
- 1. Bank Exams and SSC Percentages – Concept Session www.georgeprep.com 1
- 2. www.georgeprep.com Topics Break-up Percentage –Fraction Relationship Percentage Change calculations Successive Increases/decreases Product Constancy Partnerships 2
- 3. • Percentage –Fraction Relationship www.georgeprep.com 3
- 4. Percentage – What does it mean? www.georgeprep.com Of the total 300 students, only 150 have appeared for the exam. 4
- 5. Percentage & Fraction www.georgeprep.com Only 3/4th of the participants who registered for the event have turned up. Fraction to Percentage Percentage to Fraction 5
- 6. Percentages, fractions decimals and ratios www.georgeprep.com 50% of the students appeared for the exam Fraction Decimal Ratio 6
- 7. Percentages, fractions decimals and ratios www.georgeprep.com Fraction Percentage Equivalent 1/1 100 ½ 50 1/3 33.33 ¼ 25 1/5 20 1/6 16.67 1/7 14.28 1/8 12.5 1/9 11.11 1/10 10 Fraction Percentage Equivalent 1/11 9.09 1/12 8.33 1/13 7.69 1/14 7.14 1/15 6.66 1/16 6.25 1/17 5.88 1/18 5.55 1/19 5.26 1/20 5 7
- 9. Percentage change calculations www.georgeprep.com Percentage change = 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 𝑥 100 9
- 10. Percentage change calculations www.georgeprep.com 100 230 0 50 100 150 200 250 2003 2014 InINR Price of a movie ticketWhat is the percentage change in the price of a movie ticket from 2003 to 2014? 10
- 11. Percentage change calculations – Significant fraction www.georgeprep.com 100 230 0 50 100 150 200 250 2003 2014 InINR Price of a movie ticketSignificant Fraction Percentage change = 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 x 100 11
- 12. Percentage change calculations – Of and than www.georgeprep.com A is what percentage of B? A is what percentage more than B? 12 𝐴 𝐵 × 100 𝐴 − 𝐵 𝐵 × 100 A is what percentage less than B? 𝐵 − 𝐴 𝐵 × 100
- 13. Percentage change Vs. Percentage Point change www.georgeprep.com 30% 33% 28% 29% 30% 31% 32% 33% 34% 2000 2012 Tax rate Percentage Change in Tax rate Percentage point change in Tax rate 13
- 14. Percentage change representation As fractions As decimals www.georgeprep.com 14 (1 ± 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡) (1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡)
- 15. Problems If John’s salary were 20% higher, it would be 20% less than Smith’s. If Smith’s salary is Rs.90,000, what is John’s salary? (A) Rs.36,000 (B) Rs.40,000 (C) Rs.60,500 (D) Rs.42,850 (E) Rs.65,000 www.georgeprep.com 15 Answer: option E
- 16. Successive Increases-Decreases- Problems Bhavna decided to donate 12% of her salary to an orphanage. On the day of donation she changed her mind and donated Rs.2,400/ which was 125% of what she had decided earlier. How much is Bhavna's salary? A) Cannot be determined B) Other than those given as options C) Rs.14,750/- D) Rs.18,500/- E) Rs.16,000/- www.georgeprep.com 16 IBPS PO Main (2015) Answer: option E
- 17. Successive Increases-Decreases- Problems In an election between two candidates, one got 52% of total valid votes. 25% of the total votes were invalid. The total number of votes were 8400. How many valid votes did the other person get? (1) 3276 (2) 3196 (3) 3024 (4) Cannot be determined (5) None of these www.georgeprep.com 17 Bank of Maharashtra PO (2008) Answer: option 3
- 19. Successive increases/decreases www.georgeprep.com 19 Formula Method: 𝑥 + 𝑦 + 𝑥𝑦 100 (𝐹𝑜𝑟 𝑡𝑤𝑜 𝑠𝑡𝑒𝑝𝑠) 𝑥 + 𝑦 + 𝑧 + 𝑥𝑦 + 𝑦𝑧 + 𝑥𝑧 100 + 𝑥𝑦𝑧 1002 (𝐹𝑜𝑟 𝑡ℎ𝑟𝑒𝑒 𝑠𝑡𝑒𝑝𝑠) Decimal Method: 1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞. × 1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞. … − 1 × 100
- 20. Successive increases/decreases www.georgeprep.com 20 Increase and decrease by x% 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑜𝑓 𝑥2 100 %
- 21. Successive increases/decreases – Order matters? www.georgeprep.com 21
- 22. Successive Increases-Decreases- Problems A number is decreased by 10% and the resulting number is again decreased by 20%, what is the final percentage of decrease? 1) 25% 2) 26% 3) 27% 4) 28% www.georgeprep.com 22 SSC CGL Tier-I (2016) Answer: option 4
- 23. Successive Increases-Decreases- Problems The strength of a school increases and decreases in every alternate year by 10%. It started with increase in 2000. Then, the strength of the school in 2003 as compared to that in 2000 was 1) increased by 8.9% 2) decreased by 8.9% 3) increased by 9.8% 4) decreased by 9.8% www.georgeprep.com 23 SSC CGL Tier-II (2014) Answer: option 1
- 24. Successive Increases-Decreases- Problems Mr Shamin’s salary increases every year by 10% in June. If there is no other increase or reduction in the salary and his salary in June 2011 was ₹ 22,385, what was his salary in June 2009? 1) ₹ 18,650 2) ₹ 18,000 3) ₹ 19,250 4) ₹ 18,500 5) None of these www.georgeprep.com 24 SBI PO (2011) Answer: option 4
- 25. Successive Increases-Decreases- Problems In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was : A) 40 % B) 42 % C) 44 % D) 46 % E) 48 % www.georgeprep.com 25 SBI Clerks Main (2016) Answer: option C
- 28. Product constancy www.georgeprep.com 1. The length of a rectangle is increased by 50%, what should be the percentage decrease in the breadth to keep the area constant? 2. The length of a rectangle is decreased by 50%, what should be the percentage increase in the breadth to keep the area constant? 28 Answers: 1. 33.33% 2. 100%
- 30. Product constancy www.georgeprep.com Increases followed by decreases Decreases followed by Increases 30
- 31. Product constancy www.georgeprep.com The length of a rectangle is increased by 50%, what should be the percentage decrease in the breadth to keep the percentage increase in area at 20%? 31 Answer: 20%
- 32. Product Constancy - Problems The product of one-third of a number and 150% of another number is what per cent of the product of the original numbers? 1) 80% 2) 50% 3) 75% 4) 120% 5) None of these www.georgeprep.com 32 SBI PO (2011) Answer: option 2
- 34. Partnerships- Problems A & B start a business. B invests an amount which is Rs 500 more than A. At the end of six months from the start of business, A and B double their respective investments. If the annual profit earned was Rs. 5200 and A’s share from the annual profit was Rs. 1600, what was A’s initial investment ? A) 1000 B) 800 C) 750 D) 400 E) 800 www.georgeprep.com 34 IBPS Clerks Prelims (2016) Answer: option D
- 35. Partnerships- Problems Pihu and Rani start a business together by investing Rs. 9000 and Rs. 6300 respectively. After a certain period, Pihu withdrew from the business completely. If at the end of 2 years the total profit earned was Rs 13500 and Pihu’s share was Rs. 6750 , after how many months did Pihu withdraw from business ? A) 23 months B) 14 months C) 20 months D) 18 months E) 15 months www.georgeprep.com 35 SBI Clerks Prelims (2016) Answer: option D