## Elitmus Previous Year Questions on Percentages

Find answers at the end of every set.

### SET 1

01. | The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will be decreased by ? | |||

(a) 13.64% | (b) 15% | (c) 18.75% | (d) 30% |

02. | A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options-air conditioning, radio and power windows- were already installed. The survey found : 15 had air conditioning, 2 had air conditioning and power windows but no radios, 12 had radio, 6 had air conditioning and radio but no power windows, 11 had power windows, 4 had radio and power windows, 3 had all three options. What is the number of cars that had none of the options? | |||

(a) 4 | (b) 3 | (c) 1 | (d) 2 |

03. | At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p>0 and q>0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true? | |||

(a) p = q | (b) p < q | (c) p > q | (d) p = q/2 |

04. | The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs 441. After a second up-down cycle, the painting was sold for Rs 1944.81. What was the original prices of the painting (in Rs)? | |||

(a) 2756.25 | (b) 2256.25 | (c) 2500 | (d) 2000 |

05. | A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is ? | |||

(a) 1 | (b) 3 | (c) 4 | (d) 5 |

06. | A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs 600 from the people already solicited. The people already represent 60% of people , the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited ? | |||

(a) 300 | (b) 250 | (c) 400 | (d) 500 |

07. | Forty percent of the employees of a certain company are men and 75% of the men earn more than Rs 25,000 per year. If 45% of the company’s employees earn more than Rs 25,000 per year, what fraction of the women employed by the company earn Rs 25,000 per year ? | |||

(a) 2/11 | (b) 1/4 | (c) 1/3 | (d) 3/4 |

08. | In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals : I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals? | |||

(a) 10 | (b) 12 | (c) 17 | (d) 22 |

09. | One bacteria splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produce next generation. If the seventh generation number is 4096 million, what is the number in the first generation? | |||

(a) 1 million | (b) 2 million | (c) 4 million | (d) 8 million |

10. | I bought 5 pens, 7 pencils and 4 erasers. Rahul bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens ? | |||

(a) 37.5% | (b) 62.5% | (c) 50% | (d) None of these |

Answers : Find Detailed Solutions at the end of the the page.

1. | D | 2. | D |

3. | C | 4. | A |

5. | C | 6. | A |

7. | D | 8. | C |

9. | A | 10. | B |

### SET 2

01. | Ram sells his goods 25% cheaper than Shyam and 25% dearer than Rahul. How much percentage is Rahul’s goods cheaper than Shyam’s ? | |||

(a) 33.33% | (b) 50% | (c) 66.66% | (d) 40% |

02. | In an election between 2 candidates, Bhiku gets 65% of the total valid votes. If the total votes were 6000, what is the number of valid votes that the other candidate Mhatre gets if 25% of the total votes were declared invalid ? | |||

(a) 1625 | (b) 1575 | (c) 1675 | (d) 1525 |

03. | In an examination, Mohit obtained 20% more than Sushil but 10% less than Rajesh. If the marks obtained by Sushil is 1080, find the percentage marks obtained by Rajesh if the full marks is 2000. | |||

(a) 86.66% | (b) 72% | (c) 78.33% | (d) 77.77% |

04. | The population of the village of Gavas is 10,000 at this moment. It increases by 10% in the first year. However, in the second year, due to migration, 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 |

05. | 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 (counting the final score of the students). | |||

(a) 37.26 | (b) 37.6 | (c) 37.8 | (d) 36.93 |

06. | Ram spends 20% of his monthly income on his household 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 the monthly income ? | |||

(a) 10000 | (b) 15000 | (c) 20000 | (d) 12000 |

07. | Hans and Bhaskar have salaries that jointly amount to Rs 10,000 per month. They spend the same amount monthly and then it is found that the ratio of their savings is 6:1. Which of the following can be Hans’s salary ? | |||

(a) Rs 6000 | (b) Rs 5000 | (c) Rs 4000 | (d) Rs 3000 |

08. | 4/5th of the voters in Bellary promised to vote for Sonia and the rest promised to vote for Sushma. Of these voters, 10% of the voters who had promised to vote for Sonia, did not vote on the election day, while 20% of the voters who had promised to vote for Sushma did not vote on the election day. What is the total no. of votes polled if Sonia got 216 votes ? | |||

(a) 200 | (b) 300 | (c) 264 | (d) 100 |

09. | 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 appeared in the examination ? | |||

(a) 500 | (b) 400 | (c) 300 | (d) 600 |

10. | Ravana 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 Ravana’s salary ? | |||

(a) Rs 11,494.25 | (b) Rs 20,000 | (c) Rs 10,000 | (d) Rs 15,000 |

Answers : Find Detailed Solutions at the end of the the page.

1. | D | 2. | B |

3. | B | 4. | B |

5. | B | 6. | C |

7. | A | 8. | C |

9. | A | 10. | C |

### SET 3

01. | A man earns x% on the first Rs 2,000 and y% on the rest of his income. If he earns Rs 700 from Rs 4,000 and Rs 900 from Rs 5,000 of income, find x%. | |||

(a) 20% | (b) 15% | (c) 25% | (d) None of these |

02. | The price of a Maruti Car rises by 30% while the sales of the car comes down by 20%. What is the percentage change in the total revenue ? | |||

(a) -4% | (b) -2% | (c) +4% | (d) +2% |

03. | A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance, he purchases oranges. Number of oranges he can purchase? | |||

(a) 36 | (b) 40 | (c) 15 | (d) 20 |

04. | 2/5 of the voters promise to vote for P and rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then, the total number of voters is ? | |||

(a) 100 | (b) 110 | (c) 90 | (d) 95 |

05. | The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls and the Praja Party lost by a majority twice as large as that by which it had won the Assembly polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the previous Assembly Polls ? | |||

(a) 1,10,000 | (b) 1,50,000 | (c) 1,40,000 | (d) 1,20,000 |

06. | The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994 is Rs 20 per kg. The inflation rates of the years 1994 and 1995 are expected to be 8% each. the expected price of sugar price on January 1, 1996 would be ? | |||

(a) Rs 23.60 | (b) Rs 24.00 | (c) Rs 24.20 | (d) Rs 24.60 |

07. | A report consists of 20 sheets each of 55 lines and each such line consists of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists off 70 characters. The percentage reduction in number of sheets is closet to | |||

(a) 20% | (b) 5% | (c) 30% | (d) 35% |

08. | To pass an examination, 40% marks are essential. A obtains 10% less than the pass marks and B obtains 11.11% marks less than A. What percent less that the sum of A’s and B’s marks should C obtain to pass the exam ? | |||

(a) 40% | (b) 41(3/17)% | (c) 28% | (d) Any of these |

09. | The hourly wages of a female labour are increased by 12.5%, whereas the weekly working hours are reduced by 8%. Find the percentage change in the weekly wages if she was getting Rs 1200 per week for 50 hours previously. | |||

(a) +3.5% | (b) 4% | (c) 4.5% | (d) None of these |

10. | Two numbers X and Y are 20% and 28% less than a third number Z. Find by what percentage is the number Y less than the number X. | |||

(a) 8% | (b) 12% | (c) 10% | (d) 9% |

### Answers : Find Detailed Solutions at the end of the the page.

1. | B | 2. | C |

3. | D | 4. | A |

5. | C | 6. | C |

7. | A | 8. | D |

9. | A | 10. | C |

1. Let the length, breadth and height of the room be 3,2 and 1 unit respectively. Area of the four walls of the room = 2(l + b) h =2 (3 + 2) x 1= 10 sq unit New length, breadth and height of the room will be 6, 1 and 1/2 unit respectively. Hence, new area of the four walls of the room = 2 (6+1) x 0.5= 7 sq unit. Percentage decrease (%) = 10-7/10=30 (D) |

5. Let the marks scored in five subjects be 6a, 7a, 8a, 9a and 10a. Total marks in all the five subjects= 40a Max marks of the five subjects= 40a/0.6 (40a is 60% of total marks) Hence, Max marks in each subject = 40a/(0.6 x 5)= 13.33a Hence Percentage in each subject (%)= *multiply each value by 100. 6a/13.33a= 45.01% 7a/13.33a= 52.51% 8a/13.33a= 60.01% 9a/13.33a=67.51% 10a/13.33a=75.01% Number of papers in which he got more than 50% marks is 4. (c) |

6. Let a be the number of people who were asked for donations. People already solicited= 0.6a Remaining people= 0.4a Amount collected from the people solicited= 600 x 0.6a= 360a which is 75% of the amount to be collected. Remaining amount 25%= 120a Average donation from remaining people = 120a/0.4a=300 (a) |

7. Let number of men and women be 40 and 60 respectively. » Number of men earning more than Rs 25,000 = 30 »Total number of employees earning more then Rs 25,000 = 45 »Number of women earning more than Rs 25,000= (45 – 30)= Rs 15 »Now, fraction of the women earning Rs 25,000 or less = (60 – 15)/60 = 45/60 = 3/4 (d) |

10. Pens=A Pencil=B Eraser=C Let, 5A + 7B + 4C = 100 —-(1) then, 6A + 14B + 8C = 150 —-(2) Mutliplying equation (1) and (2) 10A + 14B + 8C = 200 Now after solving equation (1) and (3) We get, A=12.5 Hence, total amount paid for 5A=12.5 x 5=62.5 Hence, Percentage of the total amount paid by(%)=62.5 (b) |

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