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Percentages, Fractions, Ratio

Percentages and fractions are core topics from which you should expect questions in most MBA entrance tests such as CAT, GMAT and TANCET. Concepts usually tested include converting fractions to percentages, percentages to fractions, equating a parameter given as a percentage and as a number and percentage increase and percentage decrease. Quite often these questions are framed as word problems. Usually one to two questions appear testing this basic concept.

  1. If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?

  2. A shepherd has 1 million sheeps at the beginning of Year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheeps die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheeps. Which of the following is correct?

    1. x > y
    2. y > x
    3. x = y
    4. Cannot be determined

    Concept: Percent increase, percent decrease

  3. In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes and there are no invalid votes, by how many votes did it lose the election?

  4. A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

  5. When processing flower nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?

    1. 1.5 kgs
    2. 1.7 kgs
    3. 3.33 kgs
    4. None of these

    Concept: Mixtures and alligation

  6. A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

  7. If the cost price of 20 articles is equal to the selling price of 16 articles, what is the percentage of profit or loss that the merchant makes?

    1. 20% Profit
    2. 25% Loss
    3. 25% Profit
    4. 33.33% Loss
  8. 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?

  9. If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

  10. Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?

  11. 40% of 70 is x% more than 30% of 80. Find x.

  12. John weighs twice as much as Maria. Maria's weight is 60% of Bob's weight. Dave's weight is 50% of Lee's. Lee weighs 190% as much as John does. Which of these 5 persons weighs the least?

  13. Tina, Mina, Gina, Lina and Bina are 5 sisters, aged in that order, with Tina being the eldest. Each of them had to carry a bucket of water from a well to their house. Their buckets' capacities were proportional to their ages. While returning, equal amount of water got splashed out of their buckets. Who lost maximum amount of water as a percentage of the bucket capacity?

  14. Joan started work 2 years ago. Her starting salary was half of Mike's salary at that time. Each year since then Joan and Mike have received a rise of 10% in their respective salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary?

  15. If S is 150 percent of T, then T is what percent of S + T?

  16. The taxes for various income slabs are given below:

    Income Slab (I) Tax rate
    I ≤ 500 0
    500 < I ≤ 2000 5%
    2000 < I ≤ 5000 10%
    5000 < I < 10,000 15%

    There are 15 persons working in an organization. Out of them 3 to 5 persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the 15 person? (e.g., If one is earning Rs. 2000, the tax should be : 500 * 0 + 1500 * 0.05)

    1. 1350 to 7350, both excluded
    2. 1350 to 9800, both included
    3. 2175 to 7350, both excluded
    4. 2175 to 9800, both included
    5. None of the above
  17. A school sold drama tickets for 100 each for donating to an orphanage. One member sold 75% of his tickets and had 80 tickets left. How much money did the member collect?

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