CAT Practice : Percents, Profits

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The following topics are covered in the CAT quant section from Arithmetic in Percents and Profits. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Profit - Progressions

    A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?

    1. 24
    2. 18
    3. 27
    4. 32
  2. Percentages - Variables

    P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take?

    1. 10% to 28%
    2. 10% to 25%
    3. 10% to 37%
    4. 10% to 43%
    • Correct AnswerChoice (C).
      10% to 37%
      Correct answer
    • Explanatory Answer
    • Percents and Algebra
    • Medium
  3. Percents - Mixtures

    An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?

    1. 30% ≤ x ≤ 40%
    2. 32.5% ≤ x ≤ 42%
    3. 33.33% ≤ x ≤ 40%
    4. 32.25% ≤ x ≤ 40%
    • Correct AnswerChoice (D).
      32.25% ≤ x ≤ 40%
      Correct answer
    • Explanatory Answer
    • Percentages - Ratios
    • Medium
  4. Percentages - Integers

    A earns 25% more than B. C earns 25% more than A. A earns 20% more than D. E earns 20% more than A. A, B, C, D, and E earn integer amounts less than Rs. 100. What is the total amount earned by all five of them put together?

    1. Rs. 300
    2. Rs. 245
    3. Rs. 305
    4. Rs. 480
    • Correct AnswerChoice (C).
      Rs. 305
      Correct answer
    • Explanatory Answer
    • Percents and Fractions
    • Medium
  5. Percents - Golden Ratio

    A is x% more than B and is x% of sum of A and B. What is the value of x?

    1. 50%
    2. 62%
    3. 75%
    4. 37%
    • Correct AnswerChoice (B).
      Correct answer
    • Explanatory Answer
    • Percents - Golden Ratio
    • Medium
  6. Percentages - Variables

    A, B, C and D share a loot. A gets a% of the total. B gets b% of the remaining (after A has taken his share). C gets c% of the remaining and D gets the rest. D gets a% less than what A gets, B and C get equal amounts. b = 2a.
    1.   What percentage of what A got did C get?
    2.   If the total amount is equal to Rs. 1000, what is the difference between what A got and what D got?

    1. 160%
    2. 80%
    3. 175%
    4. 150%
  7. Percentages - Variables

    A is x% less than B, A is y% less than C. C is k% more than B. Express k in terms of x and y.

    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Percents and Algebra
    • Medium
  8. Percentages - Classroom

    In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?

    1. 25%
    2. 33.33%
    3. 40%
    4. 20%
    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Percents - Boys and Girls
    • Medium
  9. Percentages - Classroom

    Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?

    1. 33.33%
    2. 40%
    3. 25%
    4. 60%
    • Correct AnswerChoice (B).
      Correct answer
    • Explanatory Answer
    • Percents - Boys and Girls
    • Medium
  10. Profit Merchants

    Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.

    1. 25%
    2. 12.5%
    3. 37.5%
    4. 40%
  11. Percents - Golden Ratio

    a is x % of b, b is x% more than a. Find x.

    1. 50%
    2. 62%
    3. 75%
    4. 37%
    • Correct AnswerChoice (B).
      Correct answer
    • Explanatory Answer
    • Percents - Golden Ratio
    • Medium
  12. Percents - Two digit numbers

    A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.

    1. 45
    2. 54
    3. 63
    4. 72
  13. Profits - Maximum

    A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?

    1. Rs. 2160
    2. Rs. 1420
    3. Rs. 1580
    4. Rs. 2210
    • Correct AnswerChoice (C).
      Rs. 1580
      Correct answer
    • Explanatory Answer
    • P &L - Maximum profit
    • Hard
  14. Percentages - Variables

    A is x% more than B. B is y% less than C. If A, B and C are positive and A is greater than C, find the relation between x and y.

    1. y (1 - x) less than x
    2. y (1 - x) > x
    3. y (1 + x) less than x
    4. y (1 + x) > x
  15. SICI - Instalments

    Krishna borrows Rs. 45K from a bank at 10% compound interet. He repays it in three annual installments that are in arithmetic progression. He ends up paying 54K totally. How much did he pay in year 1?

    1. Rs. 16,500
    2. Rs. 19,500
    3. Rs. 21,000
    4. Rs. 18,000
    • Correct AnswerChoice (B).
      Rs. 19,500 < x
      Correct answer
    • Explanatory Answer
    • Repaying in Instalments
    • Hard
  16. Compound Interests

    On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.

    1. Rs. 2,400
    2. Rs. 2,800
    3. Rs. 2,000
    4. Rs. 1,600
    • Correct AnswerChoice (C).
      Rs. 2,000
      Correct answer
    • Explanatory Answer
    • Compound Interests
    • Hard
  17. Simple Interest and Compound Interest

    Ram deposits Rs. P with a bank at r% compound interest and sees it reach Rs.16P in 20 years. If he had invested the same amount at r% simple interest for 20 years, what would be the amount?

    1. Between Rs. 2P and 2.5P
    2. Between Rs. 2.5P and 3P
    3. Between 3P and 3.5P
    4. Between 3.5P and 4P
    • Correct AnswerChoice (D).
      Between 3.5P and 4P
      Correct answer
    • Explanatory Answer
    • Simple Interest and Compound Interest
    • Medium
  18. Simple Interest and Compound Interest

    Ram earns an interest of 600 over two years on a simple interest basis. On a compound interest basis, at the same interest rate, he would earn Rs. 630. What is the rate of interest?

    1. 5 %
    2. 20%
    3. 30%
    4. 10%
    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Simple Interest and Compound Interest
    • Easy
  19. Profit Percent

    Ram sells onions in the streets of Chandni Chowk. Due to recent shortfall in the supply of onions, he doubles his selling price despite the cost price remains same for him due to a fixed price contract. He realizes that his profit have tripled. Find the original profit percent.

    1. %
    2. 100%
    3. 120%
    4. %
  20. Discount Percentage

    Given below is a question followed by three statements. Study the statements and decide which of the statement(s) is/are necessary to answer the question. What was the discount percentage given?
    I) On selling the table, for Rs 12650, 26.5 %, Profit was earned
    II) If there had been no discount, 30% would have been earned as profit.
    III) The Cost price of the table was Rs 10000

    1. Only I and II
    2. Only II and III
    3. Only I and III
    4. Any two of the above
    5. None of these.
  21. Total Number of Students

    In a practice paper at, questions were given from 5 topics. Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?

    1. 2500
    2. 2000
    3. 1600
    4. 4545
  22. Overall Change

    Tensile strength of a material A is a multiple of amount of materials a, b, c, d used. If the amount of material of a, b, c, d are changed by +30%, -30%, -25%, +25% respectively, what will be the overall change in tensile strength of A?

    1. No Change
    2. +14.68%
    3. –14.68%
    4. Depends on the initial amount of a, b, c, d
  23. Number of Balls

    A bucket has ‘a’ number of small and large balls out of which b% are black. Of the small balls, c% are black and of large balls, d% are black. Find the number of small balls in the bucket.

  24. Moneylender

    A moneylender takes advantage of difficult situation of poor people and charges 50% interest. However he never gets caught because he gives 20% of his total capital (initial capital + profit) as bribe. If in the beginning of 4th year, he has a capital of Rs 25,000 to invest, how much bribe did he give at the end of 2th year?

    1. Rs 4,900
    2. Rs 5,200
    3. Rs 5,000
    4. Rs 6,000
  25. Number of Students

    In an examination, 35% of students failed in quants and 42% of students failed in verbal while 14% failed in both the topics. If 222 students passed in both the topics, how many students appeared to write the examination?

    1. 500
    2. 600
    3. 700
    4. 800
  26. Percentage Change

    A solid cube made of steel is melted and recast such that its length, breadth and height changes as +10%, +10%, -20%. What is the percentage change in surface area of this cube?

    1. No change
    2. +1%
    3. -2%
    4. -1%
  27. Party A and B

    In a local election, 2400 people were to vote for Party A or Party B. Party A was bound to win the election. However, on Election Day, 33% of the voters of Party A were kidnapped. Party B was also able to influence the remaining Party A voters and thus double the strength of its voters. In this way, Party A lost by a majority which was half of that by which it would have won had the elections been fair. How many people finally voted for Party A and Party B?

    1. 600(A), 1200(B)
    2. 300(A), 600(B)
    3. 450(A), 900(B)
    4. 600(A), 900(B)
  28. Concert - Ticket Price

    Recently a band was to perform in India. However, there was widespread criticism of the high cost of its tickets so the organizers decided to offer the following discounts:

    The tickets were originally priced at Rs 25,000/ticket. Any additional tickets (above the lot sizes) were billed at the original price.A college group wants to buy 13 tickets, what is the minimum average ticket price they would need to pay (approx.)?

    1. 23,375
    2. 23,367
    3. 23,380
    4. 23,400
  29. Concert - Ticket Price

    In the previous question, what would be the minimum price (approx) per ticket if the group wanted to buy 36 tickets?

    1. 23,300
    2. 23,250
    3. 23,166.67
    4. 23,500
  30. Ice Cream Factory

    In an ice-cream factory, 30% of total Vanilla-flavored ice-cream produced is mixed with 40% of total Banana-flavored ice-cream produced, in a ratio of 1:1. Find the overall percentage of ice-cream produced which is mixed with each other. (Ice-creams of only these 2 flavors are produced in the factory)

    1. 17.14%
    2. 34.28%
    3. 35%
    4. More information required
  31. Travel Expenses

    Hari prepares a budget to visit London. However, he spends 12% of his budget on the first 10% days of his travel when he stays in the city. He knows that he has to spend another 35% of days in city itself, after which he would travel to the country side. What should be the minimum decrease in spending in country side as a percentage of his spending in city so as to complete his travel on the initial budget itself?

    1. 33.33%
    2. 30.3%
    3. 25%
    4. 32.23%
  32. Worker Efficiency

    In a field, two workers are planting trees. After sometime, a third worker is added and the number of trees planted becomes half as large. How many trees can the second worker plant as a percentage of the number of trees planted by first worker if it is given that efficiency of second worker is 1/3 of 1st and 3rd worker combined.

    1. 65%
    2. 60%
    3. 70%
    4. 75%
  33. Burger Competition

    A, B and C participated in a burger eating competition. A beat C by 18 burgers. A also beat B by eating 50% more burger than B. Also B had eaten 5 percentage points more burger than C. Find the overall number if burgers that were eaten.

    1. 90 burgers
    2. 81 burgers
    3. 72 burgers
    4. 100 burgers

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