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Percentage 01

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 :

1. D 2. D
3. C 4. A
5. C 6. A
7. D 8. C
9. A 10. B

 Detailed Solution

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  1. khushboo.bawne

    Q5 : Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
    Total marks obtained= 40x
    Max. Marks of the five subjects = 40x/0.6 [40x is 60% of total marks]
    Max. Marks in each subject = 40x/0.6*5 = 13.33x
    Hence, % of each subject = 6x*100/13.33 = 45.01%
    Or, 7x*100/13.33 = 52.51
    In same way other percentage are 60.01%, 67.52%, 75.01%.
    Hence, number of subjects in which he gets more than 50% marks = 4

  2. Niketan Moon

    Ans 3: Assume p% to be any value. and let q% be q
    Now solve the equation
    108 = (108+p% of 108) – q[108+p% of 108];
    I took p =11.11%
    108 = (108 + 12) – q[108+12]
    Solving this we get q=10.
    That means p>q.

  3. Niketan Moon

    Ans 10: Assume I paid Rs 100.
    Therefore Rahul paid Rs 150 (according to the condition)
    pen=x pencil=y eraser=z
    5x + 7y + 4z = 100 and
    6x + 14y + 8z = 150
    Solving this we get x = 12.5
    But total amount for 5 pens =5 * 12.5=62.5
    This is the % amount he has to pay.
    Ans is (b)

  4. Naveen Kumar chaurasia

    3. according to condition 108=108(1-q/100)^5(1+p/100)^4
    p & q are small so (1-5q/100)(1+4p/100)=1
    1+4p/100-5q/100=1 (neglect pq/10000)
    4p=5q i.e p:q=5:4 i.e p>q

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