01 Percentage

01 Percentage How to change % into fraction 1 1 1 1 = 33 % =8 % 3 3 12 3 20% = 20 100 = 1 5 1 =25% 4 1 9 3 1 =7 % = 37 % 13 13 8 2 25% = 25 100 = 1 4 1 = 20% 5 1 1 =7 % 14 7 40% = 40 100 = 2 5 1 2 =16 % 6 3 1 2 4 1 =6 % =57 % 15 3 7 7 = 70 100 = 7 10 1 2 =14 % 7 7 1 1 =6 % 16 4 5 3 =71 % 7 7 1 1 = 12 % 8 2 1 =5% 20 1 1 =11 % 9 9 1 1 =4 % 24 6 1 =10% 10 1 =4% 25 70% 16 14 2 %= 3 2 %= 7 50 % = 3 100 %= 7 1 6 1 7 How to change the fraction into % of 50 2 1 1 × 100 = = 16 %  6 6 3 3 1 1 100 1 × 100 = % = 11 %  9 9 9 9 The following fractions are generally used in exams. So, I recommend you to remember these fractions. These fractions are very useful to solve the lengthy questions with in time. 1 =50% 2 1 1 1 1 =9 % =2 % 40 2 11 11 5 1 then go to 9 9 æ 1ö 1 1 ÷% = 11 % = çç11 + 9 ÷ è ø 9 9 1 1 × 100 = 25%  4 4 5 5 = 55 % 9 9 (ii) Find the % value of 3 8 æ 1ö 1 1 ÷% = 12 % = çç12 + 2 ÷ è ø 8 2 3 3 1 1 = 36 + = 36 + 1 = 37 % 8 2 2 2 (iii) = 80 + 3 (iv) 1 1 % = 83 % 3 3 Find the % value of 2 3 æ 1ö 1 1 ÷% = 33 % = çç 33 + 3 ÷ è ø 3 3 5 1 =62 % 8 2 These are Basic Fraction. If I want to know the % value (i) 1 1 × 100 = 20%  5 5 1 1 = 2% 50 2 2 2 = 66 + = 66 % 3 3 3 (v) Find the % value of 5 8 1 1 1 = 12 % = 12 + 8 2 2 5 5 1 1 =60 + = 60 + 2 = 62 % 8 2 2 2 (vi) Find the % value of 4 7 1 2 2 = 14 % = 14 + % 7 7 7 4 8 1 1 = 56 + % = 56 + 1 = 57 % 7 7 7 7 (vii) Find the % value of 7 12 1 1 1 =8 %=8+ % 12 3 3 7 7 1 1 = 56 + = 56 + 2 = 58 % 12 3 3 3 (viii) Find the % value of 11 15 1 2 2 =6 %=6+ % 15 3 3 5 Find the % value of 6 11 22 = 66 + % 15 3 1 2 2 = 16 % = 16 + 6 3 3 = 66 + 7 5 10 = 80 + 6 3 (ix) 1 1 % = 73 % 3 3 9 Find the % value of Percentage 16 1 1 1 =6 %=6+ % 16 4 4 1 23 24 = – 12 12 12 9 9 1 = 54 + = 54 + 2 % 16 4 4 = 200% – 8 = 56 (x) 1 % 4 (v) Find the % value of 7 40 (ii) Find the % value of (ii) 35 8 35 32 3 = + 8 8 8 1 1 = 400% + 37 % = 437 % 2 2 (iii) Find the % value of 23 12 23 12 11 = + 12 12 12 = 100% + 91 2 2 % = 191 % 3 3 616 2 % 3 616 2 2 % = 600% + 16 % 3 3 2 % 3 2 2 % = 300% + 66 % 3 3 2 11 = 3 3 Find the fraction value of 208 1 % 3 1 %=5 2 1 3 %= 2 8 1 %=3 2 QUESTIONS BASED ON FRACTION 1 % of a number is added 2 with itself then result becomes 1320. Find the original number. Detailed Method : Let the original number be x According to the question, 1. If 37 x + x × 37 x+x× 1 % = 1320 2 3 = 1320 8 11x = 1320 8 8 = 960 11 Fraction Method: x = 1320 × 37 1 1 208 % = 200% + 8 % 3 3 =2+ 1 25 = 12 12 Alternatively: How to understand the actual meaning of fraction. Percentage 1 5 %= 2 8 means 8 × 62  37 2 %=1 7 8 x  3x = 1320 8 =3+ (iv) 2 1 %= 7 7 means 8 × 37 1 1 % = 100% + 57 % 7 7 366 33 28 5 = + 7 7 7 (iv) 2 1 % = 683 % 3 3 4 11 =1+ = 7 7 Find the fraction value of 366 1 represents its % result 6 represent original number/value means 7 × 14  62 1 37 = 6+ = 6 6 (iii) Find the fraction value of 33 Find the % value of 7 3 3 = 400 % + 71 % = 471 % 7 7 41 6 1 157 % 7 157 2 1 %= 3 6  14 How to change % into fraction whose % value is more than 100% (i) Find the fraction value of 7 Find the % value of 5 7 5 2 +  5 5 5  100% + 40%  140% Find the % value of = 700% – 16 How to change the fraction whose % value is more than 100% (i) 1 2 % = 191 % 3 3 41 42 1 = – 6 6 6 1 1 1 =2 %=2+ % 40 2 2 æ 7ö 7 1 ÷ % = 17 % = çç14 + 2 ÷ è ø 40 2 16 3 1 %= 8 2 % result Orignal Number Original number = 8 unit Result formed = 8 unit + 3 unit 1   8  37 2 %  3   11 unit  1320 1 unit  120 So, the original number = 8 × 120 = 960 2 2. 1 If 62 % of a number is sub2 tracted from itself then result becomes 6321. Find the original number. Detailed Solution, Let the original number = x A.T.Q, Original no. = 6 unit = 6 × 708 = 4248 Substract value 1 2 –6 % = Original number 15 3 New Value = 15 – 1 = 14 unit = 5670 1 unit = 405 Original value = 405 × 16 = 6480 2 5 = 6321 8 3x = 6321 8 x = 16856 Fraction method : 62 2 % of a number is added 3 with itself then result becomes 4956. Find the original number. Sol. Let the original no. = x According to the question If 16 2 x + x ×16 % = 4956 3 x+ Sol. Value = 70 × 2 1 16 % = 6 3 % result Original number Now, New No = 6 + 1 = 7 unit = 4956 1unit = 708 1 1 3 × × 5 2 4 21 =5.25 4 If 20% of (P + Q) = 40% of (P – Q) then find P : Q = 7. Sol. 8. x = 708 × 6 = 4248 Alternate: 1 % of a number is added 9 with itself then result becomes 900 find the original number. If 11 1 Added value 1 Sol. + 11 % = 9 Original number 9 New value = 9 + 1 = 10 unit = 900 1 unit = 90 Original no. = 90 × 9 = 810 6. What is 20% of 50% of 75% of 70? x = 4956 6 7x = 4956 6 3 5. 5 1 %= 2 8 1   8  62 2 %  5    Original number = 8 unit Result formed = 8 unit – 5 unit 3 units  6321 1 unit  2107 So, original number = 8 × 2107 = 16,856 3. If 6 1 = 240 5 x = 1200 Now, x× Sol. x – x × 62 1 % = 6321 x– x× 2 % of a number is sub3 tracted from itself then result becomes 5670. Find the original number. 4. x = 36 × 4 = 144 10. If 240 is 20% of a number, then 120% of that numbe will be ? sol. Let the number be = x 20% of x = 240 20 40 (P + Q) = (P – Q) 100 100 P + Q = 2P – 2Q P – Q = 4P – Q 3Q = 1P P:Q=3:1 What is 20% of 25% of 300 ? Sol. 300 × 20 25 × = 15 100 100 9. 25% of what number is 36 ? Sol. Let the number be x then x × 25 = 36 100 1200 × 120% = 1200 × 120 100 = 1440 3 % as a 17 fraction, then it is equal to : 11. If we express 41 3 700 1 7 % = × = 17 17 100 17 12. If 125% of x is 100, then x is: Sol. 41 Sol. x × 125 =100 100 100 ´ 100 = 80 125 13. If 50% of (x - y) = 30% of (x + y) then what percent is y of x ? x= Sol. 50 30 (x - y) = (x + y) 100 100 50x – 50y = 30x + 30y 50x – 30x = 30 y + 50 y 20x = 80 y x =4 y=1 1 = 25% 4 14. If 64 is added in a number then So, y is 1 % of it7 self. Find the number. number becomes 157 Sol. 157 1 11 %= 7 7 1   7  157 7 %  11   7 unit 11 unit 4 unit  64 1 unit  16 So, the original number = 7 × 16 = 112 Percentage 15. If 930 is added in a number 4 % 9 of itself. Find the original number. then number becomes 444 4 40 Sol. 444 % = 9 9 = 10% 18. If the sides of a square is increased by 40%. Find the % change in its area. Sol. 4 4 444  400%  44 % 9 9 4 40 4  9 9 4 and 9 × 444 %  40 9 Original number 9 unit 4 × 100 40 % change in Area = Side 5 Area (Side)2 25 7 49 +24 24 % change in Area = ×100 = 96% 25 +25% 100 125 Percentage decrease in consumption \ 25 ´ 100 = 20% = 125 17. If the length of a rectangle is 1 % and its 2 breadth is decreased by 20%. Find the % change in the area. increased by 37 Sol. Length × Breadth 11 × × 5 4 3  1 37 2 %  8    Percentage Sol. Price Consumption Expenditure 6 × 5 = 30  2 1 –2 16 3 %  6  7 × 4 = 28 2 2 ×100 = 6 % 30 3 20. The sale of a cinema ticket is –25 8 2 by 16 % and; the consump3 tion of a family is decreased by 20%. Find the % change in his expenditure. = = = = Area 40 44 1  20%  5    +4 1 % and the 7 price of ticket is increased by increased by 57 2 16 %. Find the % change in 3 his revenue. Sol. Sale 7 × 11 57 × L B Area Price 6 7 1 4 %= , 7 7 = 42 = 77 16 +35 2 1 %= 3 6 Required%= 26  100 100 = 26%  (Increase) 22. If one of the sides of rectangle 1 increased by 37 % and the 2 other is decreased by 20% find the percent value by which area changes. Sol. Area = Length × Breadth 1 3 Length = 37 %  2 8 Breadth = –20%  L B Area 8 × 5 = 40 11 × 4 = 44 Required % = 35 1 ×100  83 % 42 3 21. If one of the sides of a rectangle is increased by 20% and the 1 5 4 4  100 = 10%  40 (Increase) 23. A number is first reduced by 20% and then it is increased by 80%. What was the net effect? Sol. –20% = –1 , 5 4 5 +80% = +4 , 5 5 25 % Change in his revenue  26 6 × 21 = 126 % change in his expenditure 7.50 - 6 = ×100 = 25% 6 1 20 5 × 20 = 100 19. The price of sugar is increased + 31unit  930 1 unit  30 So, the original number = 9 × 30 = 270 16. The price of a commodity rise from ` 6 per kg to ` 7.50 per kg. If the expenditure cannot increase the percentage of reduction in consumption is Sol. Percentage increase 1 5 Length +20% = Breadth +5% = 2  40%  5    Formed number 40 unit other is increased by 5%. Find the percent value by which the area changes. Sol. Area of rectangle = Length × Breadth 9 36 +11 Required % = 11  100 25 = 44% (Increase) 24. The tax imposed on an article 4 is increased by 10% and its consumption decreased by 10%. Find the percentage change in revenue from it. 1 , 10 10 11 10 1 II –10% = 10 , 100 9 99 Sol. I +10% = Required % = 1  100 100 = 1% (decrease) 25. Two numbers are respectively 20% and 50% more than a third. Now what percentage is the first of the second? Sol. Let the third number be = 100 I II III 120 150 100 Then, 120  100 = 80% 150 –1 Exercise 1. 2. 3. Student A scores 20 marks in an examination out of 30 while another student B scores 40 marks out of 70. Who has performed better ? (a) A (b) B (c) A = B (d) Can’t be determined Company A increases its sales by 1 crore rupees while company B increases its sales by 10 crore rupees. Which company has more percentage growth? (a) A (b) B (c) Both have same growth rate (d) Can’t be determined The population of a city grew from 20 lakh to 22 lakh. Find the percentage change based on the final value of population. 1 % (b) 8% 11 (c) 9% (d) 10% A sells his goods 30% cheaper than B and 30% dearer than C. By what percentage is the cost of C’s goods cheaper than B’s goods. (a) 46.15% (b) 47.15% (c) 67% (d) 67.15% The length and the breadth of a rectangle are changed by + 20% and by –10% respectively. What is the percentage change in the area of the rectangle. (a) 8% increase (b) 8% decrease 6. 7. (a) 47 5. 5 1 % 7 (b) 48 1 % 7 2 % (d) None of these 7 The cost of manufacture of an article is made up of four components A, B, C and D which have a ratio of 3 : 4 : 5 : 6 respectively. If there are respective changes in the cost of +10%, –20%, –30%, and +40%, then what would be the percentage change in the cost. (c) 47 8. (a) 9 4. (c) 10% increase (d) None of these Due to a 25% price high in the price of rice, a person is able to purchase 20 kg less of rice for Rs. 400. Find the initial price. (a) 4 Rs/kg (b) 5 Rs/kg (c) 8 Rs/kg (d) None of these A’s salary is 20% lower than B’s salary, which is 15% lower than C’s salary. By how much percent is C’s salary more than A’s salary? (a) 2 2 % 9 2 % 9 2 % 9 Rakesh Yadav receives an inheritance of a certain amount from his grandfather. Of this he loses 32.5% in his effort to produce a film. From the balance, a taxi driver stole the sum of Rs. 1,00,000 that he used to keep in his pocket. Of the rest, (c) 4% 9. (b) 3 (d) 1 he donated 20% to a charity. Further he purchases a flat in Ganga Apartment for Rs. 7.5 lakh. He then realises that he is left with only Rs. 2.5 lakh cash of his inheritance. What was the value of his inheritance ? (a) 25 lakh (b) 22.5 lakh (c) 20 lakh (d) 18 lakh 10. What is 20% of 50% of 75% of 70? (a) 5.25 (b) 6.75 (c) 7.25 (d) 5.5 3 % as a frac17 tion, then it is equal to 11. If we express 41 17 7 (b) 7 17 12 3 (c) (d) 17 17 12. Mr. Rakesh Yadav is worried about the balance of his monthly budget. The price of petrol has increased by 40%. By what percent should he reduce the consumption of petrol so that he is able to balance his budget? (a) 33.33 (b) 28.56 (c) 25 (d) 14.28 13. In Question 12, if Rakesh Yadav wanted to limit the increase in his expenditure to 5% on his basic expenditure on petrol, then what should be the corresponding decrease in consumption. (a) 33.33 (b) 28.56 (c) 25 (d) 20 (a) Percentage 14. Ram sells his goods 25% cheaper than Shyam and 25% dearer than Balram. How much percentage is Balram’s goods cheaper than Shyam’s ? (a) 33.33% (b) 50% (c) 66.66% (d) 40% 15. In an election between 2 candidates, Rakesh Yadav gets 65% of the total valid votes. If the total votes were 6000, what is the number of valid votes that the other candidate Bhuvnesh gets, if 25% of the total votes were declared invalid ? (a) 1625 (b) 1575 (c) 1675 (d) 1525 16. In a medical certificate, by mistake a candidate gave his height as 25% more than normal. In the interview pannel, he clarified that his height was 5 feet 5 inches. Find the percentage correction made by the candidate from his stated height to his actual height. (a) 20% (b) 28.56% (c) 25% (d) 16.66% 17. Arjit Sharma generally wears his father’s coat. Unfortunately, his cousin Shaurya poked him one day that he was wearing a coat of length more than his height by 15%. If the length of Arjit’s father’s coat is 120 cm then what should be the actual length of the his coat. (a) 105 (b) 108 (c) 104.34 (d) 102.72 18. A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due to this mistake. (a) 96% (b) 95% (c) 2400% (d) 200% 19. The price of an item is increased by 20 % and then decreased by 20 % . The final price as compared to original price is: (a) 20 % less (b) 20 % more (c) 4 % more (d) 4 % less 20. 50% of a% of b is equal to 75% of b% of c. Which of the following is c? Percentage (a) 1.5a (b) 0.667a (c) 0.5a (d) 1.25a 21. The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid. (a) 77% (b) 75% (c) 88% (d) 98% 22. The price of sugar is reduced by 25% but inspite of the decrease, Aayush ends up increasing his expenditure on sugar by 20%. What is the percentage change in his monthly consumption of sugar ? (a) +60% (b) –10% (c) +33.33% (d) 50% 23. When 60% of number A is added to another number B, B becomes 175% of its previous value. Then which of the following is true regarding the values of A and B ? (a) A > B (b) B > A (c) B  A (d) either (a) or (b) can true depending upon the values of A and B 24. In an election, the candidate who got 56% of the votes cast won by 144 votes. Find the total number of voters in the voting list if 80% people cast their vote and there were no invalid votes. (a) 360 (b) 720 (c) 1800 (d) 1500 25. The population of a village is 1,00,000. The rate of increase is 10% per annum. Find the population at the start of the third year. (a) 1,33,100 (b) 1,21,000 (c) 1,18,800 (d) 1,20,000 26. The population of the Mukherjee Nagar is 10,000 at this moment. It increases by 10% in the first year. However, in the second year, due to immigration, the population drops by 5%. Find the population at the end of the third year if in the third year the population increases by 20%. (a) 12,340 (b) 12,540 (c) 1,27,540 (d) 12,340 27. Rakesh Yadav inv ests Rs. 10,000 in some shares in the ratio 2 : 3 : 5 which pay dividends of 10%, 25% and 20% (on his investment) for that year respectively. Find his dividend income. (a) 1900 (b) 2000 (c) 2050 (d) 1950 28. In an examination, Rakesh Yadav obtained 20% more than Bhuvnesh but 10% less than Pawan. If the marks obtained by Bhuvnesh is 1080. find the percentage marks obtained by Pawan if the full marks is 2000. (a) 86.66% (b) 72% (c) 78.33% (d) 77.77% 29. In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (conunting the final scores of the candidates). (a) 37.266 (b) 37.6 (c) 37.8 (d) 36.93 30. Rakesh Yadav spends 20% of his monthly income on his houshold expenditure, 15% of the rest on books, 30% of the rest on clothes and saves the rest. On counting, he comes to know that he has finally saved Rs. 9520. Find his monthly income. (a) 10000 (b) 15000 (c) 20000 (d) 12000 31. Rakesh Yadav and Bhuvnesh have salaries that jointly amount to Rs. 10,000 per month. They spend the same 6 amount monthly and then it is found that the ratio of their savings is 6 : 1. Which of the following can be Rakesh Yadav’s salary ? (a) Rs 6000 (b) Rs 5000 (c) Rs 4000 (d) Rs 3000 32. The population of a village is 5500. If the number of males increase by 11% and the number of females increases by 20% then the population becomes 6330. Find the population of females in the town. (a) 2500 (b) 3000 (c) 2000 (d) 3500 33. Bhuvnesh’s salary is 75% more than Saurabh’s. Bhuvnesh got a raise of 40% on his salary while Saurabh got a raise of 25% on his salary. By what percent is Bhuvnesh’s salary more than Saurabh’s ? (a) 96% (b) 51.1% (c) 90% (d) 52.1% 34. Last year, the Indian cricket team played 40 one day cricket matches out of which they managed to win only 40%. This year, so far it has played some matches, which has made it mandatory for it to win 80% of the remaining matches to maintain its existing winning percentage. Find the number of mathes played by India so far this year. (a) 30 (b) 25 (c) 28 (d) Insufficient Information 35. In the recent, climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian. (a) 73% (b) 77% (c) 79% (d) 83% 36. A cow and a calf cost Rs. 2000 and Rs. 1400 respectively. If the 7 price of the cow and that of the calf is increased by 20% and 30% respectively then the price of 1 dozen cows and 2 dozen calves is: (a) 72,480 (b) 71,360 (c) 74,340 (d) None of these 37. During winters, an athlete can run ‘x’ meters on one bottle of Glucose. But in the summer, he can only run 0.5x meters on one bottle of Glucose. How many bottles of Glucose are required to run 400 meters during summer ? (a) 800/x (b) 890/x (c) 96 (d) 454/x 38. Out of the total production of iron from hemetite, an ore of iron, 20% of the ore gets wast ed, and out of the remaining ore, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80,000 kg, then the quantity of hematite mined from that mine in the year is (a) 5,00,000 kg (b) 4,00,000 kg (c) 4,50,000 kg (d) None of these 39. A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2.0% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net investment of the first year ? (a) Rs 3350 (b) Rs 2500 (c) Rs 4000 (d) Rs 3212.50 40. Recently, while shopping in Mukherjee Nagar, Delhi, I came across two new shirts selling at a discount. I decided to buy one of them for my little boy Sherry. The shopkeeper offered me the first shirt for Rs. 42 and said that it usually sold for 8/ 7 of that price. He then offered me the other shirt for Rs. 36 and said that it usually sold for 7/6th of that price. Of the two shirts which one do you think is a better bargain and what is the percentage discount on it ? (a) First shirt, 12.5% (b) second shirt, 14.28% (c) Both are same (d) None of these 41. 4/5th of the voters in Delhi promised to vote for Rakesh Yadav and the rest promised to vote for Bhuvnesh. Of these voters, 10% of the voters who had promised to vote for Rakesh Yadav did not vote on the election day, while 20% of the voters who had promised to vote for Bhuvnesh did not vote on the election day. What is the total number of votes polled if Rakesh Yadav got 216 votes ? (a) 200 (b) 300 (c) 264 (d) 100 42. In an examination, 80% students passed in Physics, 70% in Chemistry while 15% failed in both the subjects. If 325 students passed in both the subjects. Find the total number of students who apperared in the examination. (a) 500 (b) 400 (c) 300 (d) 600 43. Rakesh Yadav spends 30% of his salary on house rent, 30% of the rest he spends on his children’s education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs. 2500. What is Rakesh Yadav’s salary ? (a) Rs 11,494.25 (b) Rs. 20,000 (c) Rs 10,000 Percentage (d) Rs.15,000 44. The entrance ticket at the Batra cinema in Delhi is worth Rs. 250. When the price of the ticket was lowered, the sale of tickets increased by 50% while the collection recorded a decrease of 17.5%. Find the deduction in the ticket price (a) Rs 150 (b) Rs. 112.5 (c) Rs 105 (d) Rs. 120 45. Rakesh Yadav’s monthly salary is A rupees. Of this , he spends X rupees. The next month he has an increase of C% in this salary and D% in his expenditure. The new amount saved is: (a) A(1+C/100) – X (1+D/100) (b) (A/100) (C – (D) X (1+D/100) (c) X(C – (D)/100 (d) X(C + D)/100 46. In the year 2000, the luxury car industry had two car manufactures – Maruti and Honda with market shares of 25% and 75% respectively. In 2001, the overall market for the product increased by 50% and a new player BMW also entered the market and captured 15% of the market share. If we know that the market share of Maruti increased to 50% in the second Percentage year, the share of Honda in that year was: (a) 50% (b) 45% (c) 40% (d) 60% 47. Ambani, a very clev er businessman, started off a business with very little capital, In the first year, he earned a profit of 50% and donated 50% of the total capital (initial capital + profit ) to a charitable organisation. The same course was followed in the 2nd and 3rd years also. If at the end of three years, he is left with Rs. 16,875, then find the amount donated by him at the end of the 2nd year. (a) Rs 45,000(b) Rs 12,500 (c) Rs 22,500 (d) Rs 20,000 48. In an examination, 48% students failed in Hindi and 32% students in History, 20% students failed in both the subjects. If the number of students who passed the examination was 880, how many students appeared in the examination if the examination consisted only of these two subjects ? (a) 2000 (b) 2200 (c) 2500 (d) 1800 49. At IIM Bangalore, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. if the number of those getting a fee waiver is 90, find the total number of students getting 50% concession if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession? (a) 360 (b) 280 (c) 320 (d) 330 50. A machine depreciates in value each year at the rate of 10% of its previous value. However, every second year there is some maintenance work so that in t h a t particular year, depreciation is only 5% of its previous value. If at the end of the fourth year, the value of the machine stands at Rs. 1,46,205, then find the value of machine at the start of the first year. (a) Rs 1,90,000 (b) Rs 2,00,000 (c) Rs 1,95,000 (d) Rs 2,10,000 8 Solution 1. (a) % Marks score by the student A = 5. Length × Width = Area Old 10 10 = 100 +20% –10% New 12 9 = 108 Increased in Area = 108 – 100 = 8 20 2 ×100 = 66 % 30 3 % Marks score by the student B = 40 1 ×100 = 57 % 70 7 Now it is clear that the performance of A is better. Alternatively  (a) Out of 30 7 Marks Score 20×7 A B 40×3 70 3 4. 2 100 ×100 = % = 10% 20 10 70 : 100 : 700 13 Note:- Make the ratios in such a way that can not generate fractions:  Multiply 13 in all ratios. A : B : C 910 : 1300 : 700 The percentage by which C’s price is cheaper than B’s price= = 9 1300 – 700  1300 600 = 46.15% 13 Alternatively  Note:- In such type of questions we can use the below given formula.   Shows increase   – Shows decrease    XY    X + Y+ 100    Change in area = 20 – 10 – 6. 20  10 = 8% 100 Sign is +ve so increase in area = 8% (a) According to the question :Rise in the price = 25% % Reduction in consumption = 25 ×100 = 20% 125 But actual reduction in consumption = 20kg  20% = 20 kg 1% = (a) Let the price of B = Rs. 100 Now According to the question :A : B : C 8 ´ 100 = 8% Ans. 100 % increased = 210 Note:- Equal the out of marks then we can directly analyse the performance. Marks Score Out of A  140 210 B  120 210 Now we can say performance of A is better. 2. (d) Apparently, the answer to the question seems to be company B. The question can not be answered since we don’t know the previous year’s sales figure. 3. (d) Percentage change based on the final value = (a) Let 20 kg 20 original consumption (100%) = 20 ×100 20 = 100 kg Money spent = 400 Rs (Given) Original price = Alternatively:- 400 = Rs 4/kg 100 Let the expenditure = 100 Rs 100 +25 –25 125 ×100  5 = 125 1 4 New = 5 5  Original 1 unit  20 kg Percentage Original consumption = 20 × 5 = 100 kg New consumption = 4 × 20 = 80 kg Original price of the rice = 7. 400 = Rs 4/kg 100 (a) Note :- In such type of question try to make ratio between all the given variables. Ratio of Salary A 4 : B B : 5 17 1 : C –20% = 5 : 20 3 15% = 20 4 : = 8. 100 – 68  68 Old cost  B 300 : 400 +10% New cost  330 : ×100 C : –20% 500 –30% 320 350 : D : 600 +40% 840 Total old cost = (300+400+500+600) = 1800 Rs. Total New cost = (330+320+350+840) = 1840 Rs. % Change = 9. 1840 – 1800  1800 40 2 ×100 = = 2 % 18 9 (c) Let the inheritance value Recieved by Rakesh Yadav = x According to the question:-   100 – 32.5  – 100000  × 80 x  100   100 = 41 1 1 3   = 5 2 4 21 = 5.25 4  697  3  1 700 3 %=  =  17 17  100   100 17 7  =   17  (a) Note :- In such type of questions assume any value but ratio should not be changed. : 13.5 Lakh –1 Lakh 12.5 Lakh 2.5 Lakh –7.5 Lakh 10 Lakh –20% Same as mention in question. So option (c) is correct. 11. (b) 32 8 800 1 ×100 = ×100 = = 47 % 68 17 17 17 A –32.5% 5 B: C 17 : 20 A : B : C Ratio 68 : 85 : 100 C’s salary more than A = 20 lakh 10. (a) Value = 70  Combine the ratio of salary :- A: B AlternativelyNote:- These type of problems should either be solved through the reverse process or through options. Option (c):- Total value of inheritance = 20 lakh According to the question:- 12. (b) Note  (1) If the price of a commodity increases by r %, then the reduction in consumption so as not to increase the expenditure is =   r  100  %   100  r   (2) If the price of a commodity decreases by r% then increase in consumption, so as not to decrease expenditure on this item is =   r  100  %   100 – r   Use above these two methods to save your valuable time. % Reduction in consumption = = 40 400 200  100 = = = 28.57% 140 14 7 13. (c) Let the expenditure = 100 Rs. After increase of 40% = 140 Rs. According to the question, Increase in expenditure should be only 5%= 105 (750000 + 250000) 67.5   80  x  100 – 100000   100 = 1000000   40 100  40  % Reduction = 140 – 105  140  100 x = 2000000, x = 20 Lakh Percentage 10 % Reduction = 14. (d) 35  100 = 25% 140 Ram : Shayam Ram : Bram 5 : 4 3 : 4 1   25% = 4   Note :- The price of Ram’s goods should be equal in both cases. So equal the prices. Ram : Shyam : Bram 15 : 20 : 12 % Bram’s goods cheaper than Shyam’s  20 – 12 = 20 ×100 = 40 % 15. (b) Let the total number of valid votes get by Bhuvnesh = x According to the question:- 75 100–65 75 35   = 6000  100 100 100 100 x = 6000 x = 1575 16. (a) Note :- We can assume any value as the height of the candidate to save your valuable time. Let height = 4x feet After increament = 4x × 125 = 5x feet 100 % reduction in height to get original value =  5 x – 4x  5x Old 10 5 2 New 11 6 3 Volume 100 198 +98 120  100 115 5 = 1 5 Case (II):- On multiplication New number (N2) = 5×5 = 25 % change in result =  25 – 1 ×100 = 96% 25 19. (d) Let original price = 100  First new price = 120 & Final price = 80 % of 120 = 96  Final price is 4 % less than the original price. 1 a × ×b = 2 100 3 c 4 b 3 × ×c 4 100 3 c  a = 2 98  100 = 98% 100 % Change in volume = Alternatively : Let initial volume = 100 New volume = 100× 110 120 50   100 100 100 %change = 98% 22. (a) Let the initial expenditure = 100 Initial Expenditure 100 % –25 +20% New 75 Expenditure Final expenditure +45 120 % change in consumption = 120 – 75  75 ×100 45  100 = 60% 75 23. (d) According to the question :60% A + B = 175% B 3 A+B 5 New number (N1 ) = 11 Length Breadth Height = = 104.34 cm 18. (a) Let the number = 5 According to the question:Case (I):On dividing a = 2 21. (d) 0.667a  100 = 20 % 17. (c) Actual length of Arjit’s coat = 20. (b) 2 a = 3 c = = 7 B 4 3 A 5 = 3B 4 A 5 = B 4 A : B = 5:4 Apparently it seems that A is bigger, but if you consider A and B to be negative the opposite would be true. Hence option (d) is correct. 24. (d) Let the total number of votes = x According to the question :x× 80 12 × = 100 100 144 Percentage 27. (d) Ratio of shares = 2x : 3x : 5x According to the question, (2x + 3x + 5x) = 10,000 10x = 10,000 x = 1000 Ist share = 2×1000 = 2000 Rs. IInd share = 3×1000 = 3000 Rs. IIIrd share = 5×1000 = 5000 Rs. Divident income 144  100  100 x = = 1500 80  12 Total votes = 1500 Alternatively :(d) Let the cast votes = 100 100 Winner 56 Loser 44 12 Total number of votes = = 200 + 750 + 1000 = 1950 28. (b) 20% = 1200  100 = 1500 80 Old population New population Ist year 10 11 nd II Year 10 11 100 121 According to the question:100 units = 100,000 1 unit = 1000 121 units = 121 × 1000 = 121,000 Alternatively:(b) Let the population at the start of the third year = x x = 100,000 × 110 110 × 100 100 New population = 10,000× 110 95 120 × × 100 100 100 = 12,540 Alternatively :- (b) Old 10 20 5____ 1000 According to the question :1000 units = 10000 1 unit = 10 Total New population = 1254×10 Percentage 10% = 1 10 According to the question :- Ist year IInd year IIIrd year Marks of Rakesh Yadav will be equal in both cases. Rakesh Yadav : Bhuvnesh : Pawan Ratio of marks:18 : 15 : 20  × 72 1080 Marks obtained by Pawan = 20×72 = 1440 % marks = New 11 19 _6__ 1254 = 12540 1440  100 = 72% 2000 29. (b) Passing marks = 33 [Given] Let the total number of Students = 100 According to the question:avg. = x = 121,000 26. (b) The population of Mukherjee Nagar = 10,000 (+10%) (–5%) (20%) 1 , 5 Rakesh Yadav : Bhuvnesh Rakesh Yadav : Pawan 9 5 : : 10 6 Marks 1 10 25. (b) 10% = 2000  10 3000  25 5000  20 + + 100 100 100 = 12 units = 144 1 unit = 12 Total cast votes = 12×100 = 1200 According to the question :- avg. = 30   33 – 20   10  33  35  60 100 30  13  330  2100 75 390  330  2100 = 37.6 75 30. (c) Let the monthly income of Rakesh Yadav = Rs x. According to the question :- = 80 85 70   = 9520 100 100 100 x = 20,000 Monthly income of Rakesh Yadav = Rs. 20,000 31. (a) The only logic for this question is that Rakesh Yadav’s salary would be more than Bhuvnesh’ salary. Thus, only option (a) is possible for Rakesh Yadav’s salary. 32. (a) population of the village = 5500 x× 12 After increament new population of the village = 6330 % increment = =  6330 – 5500  5500  100 = (700+500+800) = 2000 Total people who were = 560 + 300+720 = 1580 830 166 = % 55 11 : Male% 11% Female% 20 % 166 % 11  166   11 – 11   : 166    20 – 11    6 : 5 = 11 According to the question:11 units = 5500 1 unit = 500 Number of females = 500×5 = 2500 33. (a) Bhuvnesh : Saurabh Ratio of salary = 700 : 400 é 3ù êë 75%= 4 ú û 36. (a) Old Cost  1580  100 = 79% 2000 1 Calf 1400 1 Cow: 2000 : 980 1 metre = salary = 34. (d) The data is in-sufficient since the number of matches to be played by India this year is not given. ( You can not assume that they will play 40 Matches). 35. (c) men : women : children 700 : 500 : 800 60% Not Indian  560 300 Total people inside the premises 13 1 ×400 0.5x 90% 720 = 800 bottles x 38. (b) Let the total quantity of hematite mined =100 kg. According to the question:- 100 kg –20% wasted 80 kg re pu Non % 25 iron pure kg 20 480 480  100 = = 96% 500 5 80% 1 bottle 0.5x 400 metres = 500 +480 Percent of Bhuvnesh’s salary more than Saurabh’s +30% New Cost  2400 1820 According to the question :Price of 1 dozen cows = 2400×12 = 28800 Price of 2 dozen calves = 1820×24 = 43680 Total cost = 28800+43680 = Rs. 72,480 37. (a) According to the question :0.5x metres = 1 bottle Note :- Assume any value of salaries which can not make fractions but remember one thing ratio should not be changed. According to the question:Bhuvnesh : Saurabh Old salary 700 : 400 +40% +25% New salary Indian % people who were not Indian = +20% Ratio of Male & Female not 60 kg  20 units = 80,000 kg 1 unit = 4,000 kg Total hematite = 100 × 4000 = 4,00,000 kg 39. (d) The total cost of truck for a year = 2,50,000 + 250,000  2 + 2000 = Rs.257000 100 To get a return of 15% he must earn annualy = 257000  15 = Rs. 38550 100 Hence, monthly rent = 38550 = Rs. 3212.50 12 40. (b) Note :- In such type of question no need to calculate actual Market price and selling price. We can simply calculate the ratio on the basis of given Percentage fractions to save our valuable time. According to the question:Condition (I) :- Let Market price = 8 Rs. 7 = 7 Rs 8  Selling price = 8 × % Discount = 8 – 7 8 1%  100 = 12 1 % 2 = 100  30 = 30 units 100 Remaining salary = (100 – 30) = 70 units Salary spent on children’s education Hence, the second shirt is a better bargain. 41. (c) Let the total number of voters = 500 Voters who vote for Rakesh Yadav = 500× 4 5 = 400 Voters who vote for Bhuvnesh = (500 – 400) = 100 Rakesh Yadav : Bhuvnesh 400 : 100 = 70  30 = 21 units 100 Salary spent on clothes = 100× 20% [40] [20] Remaining Voters who voted = (500 – 60) = 440 Vote got by Rakesh Yadav = (400 – 40) = 360 According to the question:360 units = 216 216 = 360 440 units = 5% 15% 15% [Failed venn diagram of students] Total failed students = 5+15+15 = 35%  Total passed students = (100 – 35) = 65% According to the question, 65% = 325 Percentage 2500 = 25 100 Rs 100 units = 100×100 = 10000 Rs. Total salary of Rakesh Yadav = 10000 Rs. Alternatively :Total salary 100 30% Rent 24% Clothes Rem aini ng 70% 24 30 216 ×440 = 264 360  Total votes polled = 264 42. (a) Physics Chemistry 24 = 24 units 100 Remaining salary = (100) – (30+21+24) = 25 units According to the question :25 units = 2500 Rs 1 unit = 1 unit 325 ×100 = 500 65 Total number of students appeared in the examination = 500 43. (c) Let the total salary of Rakesh Yadav =100 units Salary spent on house rent 1 2 ×100 = 14 % 7 7 10% 325 65 Total students (100%) = Condition (II) :- Similarly Selling price : Market Price 6 : 7 % Discount = = 70 Education 30% 21 Total spend money = 30+21+24 = 75 Remaining salary = (100 – 75) = 25 According to the question :25  2500 1  2500 25 2500 = 10,000 Rs. 25 44. (b) Ticket price × no. of people = total collection Total salary = 100× 14 According to the question:- 100 × 100 = 10000 Rs. –17.5% +50% x x= New market share in 2001 = 100× × 150 = 8250 Rs. 8250 = 55Rs. 150 Total shares(2001) 150 % difference of ticket’s price = BMW 15% 100 – 55 ´ 100 = 45% 100 22.5 Now actual lowed price = 250× 45 = 112.5 100 Alternate:According to the question :Final sales figure :- 100 82.5 Required price drop = 150 = 67.5 = 45% 100 45 = Rs.112.5 100 100 100 100 – X 100+D  100 C  D    = A 1+  – X 1+   100   100  46. (d) Let the total Market shares in 2000 = 100 Total shares(2000) 100 15 Maruti +25% Honda 75% 25 75 50 = Rs.50 100 50 = 100 Rs. 75 Remaining Capital after Donation = (150 – 75) = Rs. 75 Initial Capital : Donation 100 : 75 First year  4 : 3 nd II year  4 : 3 IIIrd year  4 : 3 64 27 A 100+C  X 100+D  A 100+C  100× Donation given = 150× New expenditure after increament Savings = 150 = 37.5 100 Total capital = (100 + 50) = Rs. 150 45. (a) Rakesh Yadav’s monthly salary = A Rs. Expenditure = X Rs. Note :- [ Savings = Income – expenditure ] According to the question :- = Maruti Shares = 25× Profit = 150 – 82.5  New salary after increment = 90 37.5 = 60 % 90  100 150 47. (c) Let the initial capital of the businesman = Rs.100 p ro d ice Pr Required value = 250× Remaining Maruti Honda % share of Honda = 50% Sales increase 150 Collection 17.5% drop 150 = 150 100 ×625 ×625 [40,000] [16875] Capital for second year = 4 × 4 = 16 Donation for second year = 3 × 3 = 9  16 units = Rs.40,000 1 unit = 2500 Total donation = 2500×9 = Rs. 22500 Alternatively :Let the capital = x  150 50   150 50   150 50     x     = 16,875  100 100   100 100   100 100  Ist year IInd year IIIrd year Percentage  150 50   x    100 100  According to the question :(9 + 3) units = 90  150 50     = 22,500  100 100  Ist year IInd year 1 unit = 48. (b) Students failed in Hindi = 48% Students failed in History = 32% English Hindi 28% 20% The number students who are not getting waiver = (100 –12 ) = 88 units Total number of students getting 50% concession = 88 × 12% (venn diagram of failed students) Number of students passed in the examination = (100 – 60) = 40% According to the question, 40 % = 880 1% = 880 40 Total students = 880 ×100 = 40 2200 49. (d) Let the total number of students = Total students 100 Boys 60 Getting Waiver Percentage 15% 9 90 12 90 1 × 12 2  330 50. (b) Let the initial value of machine = x According to the question, x× 90 95 90 95 × × × 100 100 100 100 = 146205 x = 2,00,000 Rs. Initial value of machine = Rs. 2,00,000 Alternatively :Old value New value st I year 10 9  IInd year  20 19 IIIrd year  10 9 IVth year  20 19 40000 29241 100 ×5 ×5 2,00,000 146205 Value of machine = Rs. 2,00,000 Girls 40 7.5% 3 Getting waiver 16