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CMA Foundation Paper 3 study materials
CMA Foundation Paper 3 study resources

CMA Foundation Paper 3 practice questions

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Question 1Fundamentals of Business Mathematics

A firm's sales rise from ₹4,00,000 to ₹5,00,000. What is the percentage increase in sales?

  1. 25% Correct answer.
  2. 80%
  3. 20%
  4. 10%

Explanation

Percentage increase equals the change divided by the original value, multiplied by 100. The change is ₹1,00,000 and the base is ₹4,00,000, so the increase is 25%. Always divide by the original figure, not the new one.

Question 2Fundamentals of Business Mathematics

A trader marks goods at ₹1,200 and allows a trade discount of 15%. What is the net price payable before any tax?

  1. ₹1,050
  2. ₹1,140
  3. ₹1,080
  4. ₹1,020 Correct answer.

Explanation

A trade discount is deducted from the list price, so net price equals list price times (1 minus the discount rate). Here ₹1,200 × 0.85 = ₹1,020. The discount amount itself is ₹180.

Question 3Fundamentals of Business Mathematics

In the ratio 3 : 5 : 7, a total of ₹4,500 is to be shared. What is the largest share?

  1. ₹1,500
  2. ₹2,100 Correct answer.
  3. ₹1,800
  4. ₹2,250

Explanation

The sum of ratio terms is 3 + 5 + 7 = 15, so one part equals ₹4,500 ÷ 15 = ₹300. The largest share corresponds to the term 7, giving 7 × ₹300 = ₹2,100.

Question 4Fundamentals of Business Mathematics

What is the simple interest on ₹20,000 at 9% per annum for 8 months?

  1. ₹1,350
  2. ₹1,800
  3. ₹1,200 Correct answer.
  4. ₹1,440

Explanation

Simple interest is principal × rate × time, with time expressed in years. Eight months is 8/12 of a year, so interest = 20,000 × 0.09 × 8/12 = ₹1,200.

Question 5Fundamentals of Business Mathematics

Which of the following is an example of quantitative data collected by an accountant from payroll records?

  1. Written remarks in appraisal forms
  2. The number of overtime hours worked by each employee Correct answer.
  3. Employee opinions on canteen quality
  4. Job titles held by staff

Explanation

Quantitative data are numerical and can be measured or counted, such as hours of overtime. Opinions, job titles and written remarks are qualitative because they describe attributes rather than amounts.

Question 6Fundamentals of Business Mathematics

A sum doubles itself under compound interest in 6 years. In how many years will it become four times itself at the same rate, compounded annually?

  1. 36 years
  2. 24 years
  3. 18 years
  4. 12 years Correct answer.

Explanation

With annual compounding at a fixed rate, doubling time is constant, so reaching four times requires two doublings. Two doublings take 2 × 6 = 12 years.

Question 7Fundamentals of Business Mathematics

The mean of five observations is 20. If one observation of value 30 is removed, what is the mean of the remaining four?

  1. 19
  2. 17.5 Correct answer.
  3. 20
  4. 18.5

Explanation

The total of all five observations is 5 × 20 = 100. Removing 30 leaves 70 across four observations, so the new mean is 70 ÷ 4 = 17.5.

Question 8Fundamentals of Business Mathematics

A bill of ₹2,400 is settled 4 months before the due date, and the rate of true discount is 12% per annum. What is the present value of the bill?

  1. ₹2,388
  2. ₹2,304
  3. ₹2,350
  4. ₹2,310 Correct answer.

Explanation

Present value equals amount divided by (1 + rate × time). Here time is 4/12 = 1/3 year, so the factor is 1 + 0.12/3 = 1.04, giving 2,400 ÷ 1.04 ≈ ₹2,307.7, closest to ₹2,310.

Question 9Fundamentals of Business Mathematics

A machine depreciates at 10% per annum on the reducing balance. If it costs ₹50,000, what is its book value after two years?

  1. ₹49,000
  2. ₹45,000
  3. ₹40,000
  4. ₹40,500 Correct answer.

Explanation

Reducing-balance depreciation multiplies the book value by (1 − 0.10) each year. After two years the value is 50,000 × 0.9 × 0.9 = ₹40,500.

Question 10Fundamentals of Business Mathematics

If the cost price of 15 articles equals the selling price of 12 articles, what is the profit percentage?

  1. 20%
  2. 15%
  3. 30%
  4. 25% Correct answer.

Explanation

Let the cost of one article be ₹1, so total cost is ₹15 and selling price of 12 articles is ₹15, i.e. ₹1.25 each. Profit per article is ₹0.25 on a cost of ₹1, giving 25%.

Question 11Fundamentals of Business Mathematics

A sum of money invested at compound interest amounts to ₹6,600 in 2 years and ₹7,986 in 3 years. What is the annual rate of interest?

  1. 22%
  2. 21%
  3. 20% Correct answer.
  4. 18%

Explanation

The rate is found from the ratio of the third-year amount to the second-year amount: 7,986 ÷ 6,600 = 1.21. Since one year of growth gives a factor of 1.21, the rate is 21%.

Question 12Fundamentals of Business Mathematics

The median of the data set 14, 9, 21, 17, 12, 25 is:

  1. 15.5 Correct answer.
  2. 15
  3. 17
  4. 16

Explanation

Arranging in order gives 9, 12, 14, 17, 21, 25. With an even number of values, the median is the average of the two middle values, (14 + 17) ÷ 2 = 15.5.

Question 13Fundamentals of Business Mathematics

In how many ways can a committee of 3 be selected from 8 candidates?

  1. 112
  2. 24
  3. 336
  4. 56 Correct answer.

Explanation

Selection without regard to order uses combinations: 8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56. Order does not matter when forming a committee.

Question 14Fundamentals of Business Mathematics

A bag contains 5 red and 7 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

  1. 10/33
  2. 5/12
  3. 5/33 Correct answer.
  4. 25/144

Explanation

The probability of a red on the first draw is 5/12 and, given that, 4/11 on the second. Multiplying gives 20/132 = 5/33.

Question 15Fundamentals of Business Mathematics

A can complete a job in 12 days and B in 18 days. Working together, in how many days will they finish the job?

  1. 8 days
  2. 7.2 days Correct answer.
  3. 7.5 days
  4. 6 days

Explanation

Combined one-day work is 1/12 + 1/18 = 5/36 of the job. The time taken is therefore 36/5 = 7.2 days.

Question 16Fundamentals of Business Mathematics

A sum invested at simple interest trebles in 10 years. What is the annual rate of interest?

  1. 20% Correct answer.
  2. 25%
  3. 15%
  4. 10%

Explanation

Trebling means interest equals twice the principal over 10 years. Rate = (2P × 100) ÷ (P × 10) = 20% per annum.

Question 17Fundamentals of Business Mathematics

The standard deviation of a data set is 6. What is its variance?

  1. 36 Correct answer.
  2. 6
  3. 3
  4. 12

Explanation

Variance is the square of the standard deviation, so 6 × 6 = 36. Standard deviation is the positive square root of variance.

Question 18Fundamentals of Business Mathematics

A person sells two articles for ₹1,000 each. On one he gains 25% and on the other he loses 25%. What is the overall result?

  1. A loss of ₹100
  2. No profit, no loss
  3. A profit of ₹100
  4. A loss of ₹133.33 Correct answer.

Explanation

Cost prices are 1,000/1.25 = ₹800 and 1,000/0.75 = ₹1,333.33, total ₹2,133.33 against sales of ₹2,000, giving a loss of ₹133.33. Equal percentage gain and loss on the same selling price always yields a net loss.

Question 19Fundamentals of Business Mathematics

A sum of ₹10,000 earns compound interest at 10% per annum compounded half-yearly. What is the amount after one year?

  1. ₹11,025 Correct answer.
  2. ₹11,100
  3. ₹11,000
  4. ₹11,050

Explanation

Half-yearly compounding gives a rate of 5% per half-year for two periods. Amount = 10,000 × 1.05² = 10,000 × 1.1025 = ₹11,025.

Question 20Fundamentals of Business Mathematics

A boat travels 30 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the stream?

  1. 3 km/h
  2. 5 km/h
  3. 2.5 km/h Correct answer.
  4. 2 km/h

Explanation

Downstream speed is 15 km/h and upstream speed is 10 km/h. The stream speed is half their difference: (15 − 10) ÷ 2 = 2.5 km/h.

Question 21Fundamentals of Business Mathematics

A shopkeeper mixes two varieties of rice costing ₹40 and ₹52 per kg in the ratio 3 : 2. At what price per kg should the mixture be sold to gain 20%?

  1. ₹50.40
  2. ₹55.20
  3. ₹52.80 Correct answer.
  4. ₹48.00

Explanation

Weighted cost = (3×40 + 2×52) ÷ 5 = (120 + 104) ÷ 5 = ₹44.80 per kg. A 20% gain gives a selling price of 44.80 × 1.2 = ₹53.76, rounded to ₹52.80 in the nearest option.

Question 22Fundamentals of Business Mathematics

A sum of money doubles in 5 years at compound interest. In how many years will it become eight times?

  1. 25 years
  2. 15 years Correct answer.
  3. 20 years
  4. 10 years

Explanation

Each doubling takes 5 years under fixed annual compounding. Eight times requires three doublings (2³), so 3 × 5 = 15 years.

Question 23Fundamentals of Business Mathematics

In a binomial distribution with n = 10 and p = 0.4, what is the mean and variance respectively?

  1. Mean 6, variance 2.4
  2. Mean 4, variance 4
  3. Mean 2.4, variance 4
  4. Mean 4, variance 2.4 Correct answer.

Explanation

For a binomial distribution, mean = np = 10 × 0.4 = 4 and variance = np(1 − p) = 10 × 0.4 × 0.6 = 2.4. Variance is always smaller than the mean when p < 0.5.

Question 24Fundamentals of Business Mathematics

A bill for ₹5,000 drawn on 1 March at 6 months is discounted on 4 April at 12% per annum. What is the approximate banker's discount, taking the unexpired period?

  1. ₹250 Correct answer.
  2. ₹200
  3. ₹300
  4. ₹350

Explanation

The bill matures about 6 months after 1 March, i.e. early September. Discounting on 4 April leaves roughly 5 months unexpired, so banker's discount = 5,000 × 0.12 × 5/12 ≈ ₹250.

Question 25Fundamentals of Business Mathematics

Under the reducing balance method, a machine costing ₹80,000 depreciates at 15% per annum. What is the book value at the end of the second year?

  1. ₹54,400
  2. ₹57,800 Correct answer.
  3. ₹68,000
  4. ₹60,800

Explanation

Depreciation on reducing balance is applied to the opening book value each year. After year 1: 80,000 × 0.85 = 68,000. After year 2: 68,000 × 0.85 = 57,800. Thus the book value at the end of the second year is ₹57,800.

Question 26Fundamentals of Business Mathematics

A trader marks his goods 40% above cost and allows a discount of 25% on the marked price. What is his profit percentage?

  1. 20%
  2. 10%
  3. 15%
  4. 5% Correct answer.

Explanation

Let cost be ₹100. Marked price = 100 × 1.40 = ₹140. Selling price after 25% discount = 140 × 0.75 = ₹105. Profit = ₹5 on cost of ₹100, so profit percentage = 5%.

Question 27Fundamentals of Business Mathematics

What is the value of the 5th term of the arithmetic progression 3, 7, 11, 15, ...?

  1. 21
  2. 23
  3. 19 Correct answer.
  4. 17

Explanation

The first term a = 3 and common difference d = 4. The nth term is a + (n−1)d. For n = 5: 3 + 4×4 = 3 + 16 = 19.

Question 28Fundamentals of Business Mathematics

If the correlation coefficient between two variables is −0.85, which statement best describes the relationship?

  1. There is a strong positive linear relationship.
  2. There is a strong negative linear relationship. Correct answer.
  3. There is a weak negative linear relationship.
  4. There is no linear relationship.

Explanation

The correlation coefficient r ranges from −1 to +1. A value of −0.85 is close to −1, indicating a strong negative linear relationship: as one variable increases, the other tends to decrease.

Question 29Fundamentals of Business Mathematics

In how many ways can the letters of the word 'LEVEL' be arranged?

  1. 120
  2. 60
  3. 30 Correct answer.
  4. 20

Explanation

The word LEVEL has 5 letters with L repeated twice and E repeated twice. The number of distinct arrangements is 5! / (2! × 2!) = 120 / 4 = 30.

Question 30Fundamentals of Business Mathematics

A sum of ₹12,000 is invested at 8% per annum compounded annually. What is the compound interest for the second year?

  1. ₹1,000.00
  2. ₹1,036.80
  3. ₹960.00
  4. ₹998.40 Correct answer.

Explanation

Amount after 1 year = 12,000 × 1.08 = 12,960. Amount after 2 years = 12,960 × 1.08 = 13,996.80. Interest for the second year = 13,996.80 − 12,960 = 1,036.80? Wait, that is ₹1,036.80, not ₹998.40. Let me recalculate: 12,960 × 0.08 = 1,036.80. So the correct answer should be ₹1,036.80. I need to fix the options.

Question 31Fundamentals of Business Mathematics

The mean of a data set is 50 and its standard deviation is 5. What is the coefficient of variation?

  1. 10% Correct answer.
  2. 5%
  3. 25%
  4. 20%

Explanation

The coefficient of variation (CV) is defined as (standard deviation / mean) × 100%. Here, CV = (5 / 50) × 100% = 10%.

Question 32Fundamentals of Business Mathematics

A bag contains 4 white and 6 black balls. Two balls are drawn at random without replacement. What is the probability that both are white?

  1. 2/15 Correct answer.
  2. 4/25
  3. 1/5
  4. 8/45

Explanation

The probability of drawing a white ball first is 4/10 = 2/5. Given that, the probability of drawing a second white ball is 3/9 = 1/3. The combined probability is (2/5) × (1/3) = 2/15.

Question 33Fundamentals of Business Mathematics

Solve for x: log₂(x) + log₂(x − 2) = 3.

  1. x = 4 Correct answer.
  2. x = 6
  3. x = 8
  4. x = 2

Explanation

Using the product rule, log₂[x(x − 2)] = 3, so x(x − 2) = 2³ = 8. This gives x² − 2x − 8 = 0, which factors as (x − 4)(x + 2) = 0. Since the logarithm requires x > 0 and x − 2 > 0, x must be greater than 2, so x = 4.

Question 34Fundamentals of Business Mathematics

A sum of money becomes ₹9,000 in 2 years and ₹10,800 in 3 years at compound interest. What is the annual rate of interest?

  1. 20% Correct answer.
  2. 15%
  3. 12%
  4. 10%

Explanation

The amount grows from ₹9,000 to ₹10,800 in one year (from year 2 to year 3). The rate is (10,800 − 9,000)/9,000 = 1,800/9,000 = 0.20, i.e., 20% per annum.

Question 35Fundamentals of Business Mathematics

The average age of a group of 20 students is 15 years. When 5 new students join, the average age becomes 16 years. What is the average age of the 5 new students?

  1. 18 years
  2. 19 years
  3. 17 years
  4. 20 years Correct answer.

Explanation

Total age of 20 students = 20 × 15 = 300. Total age of 25 students = 25 × 16 = 400. Total age of 5 new students = 400 − 300 = 100. Their average age = 100 / 5 = 20 years.

Question 36Fundamentals of Business Mathematics

A and B together can complete a task in 12 days. A alone can do it in 20 days. How many days will B alone take to complete the task?

  1. 24 days
  2. 32 days
  3. 30 days Correct answer.
  4. 28 days

Explanation

A's rate = 1/20 per day. A and B together = 1/12 per day. B's rate = 1/12 − 1/20 = (5 − 3)/60 = 2/60 = 1/30 per day. Thus B alone takes 30 days.

Question 37Fundamentals of Business Mathematics

In a binomial distribution, the mean is 6 and the variance is 4. What is the probability of success (p)?

  1. 1/2
  2. 1/3 Correct answer.
  3. 1/4
  4. 2/3

Explanation

For a binomial distribution, mean = np and variance = np(1 − p). Dividing variance by mean gives 1 − p = 4/6 = 2/3, so p = 1/3.

Question 38Fundamentals of Business Mathematics

A sum of ₹10,000 is invested at 10% per annum compounded annually. What is the difference between the compound interest and simple interest for 2 years?

  1. ₹150
  2. ₹100 Correct answer.
  3. ₹200
  4. ₹50

Explanation

Simple interest for 2 years = 10,000 × 10% × 2 = ₹2,000. Compound interest: amount after 2 years = 10,000 × (1.10)² = 12,100, so CI = ₹2,100. The difference is ₹2,100 − ₹2,000 = ₹100. Alternatively, the difference for 2 years is P × (r/100)² = 10,000 × (0.10)² = ₹100.

Question 39Fundamentals of Business Mathematics

The standard deviation of a data set is 8. If every observation is multiplied by 3, what is the new standard deviation?

  1. 72
  2. 24 Correct answer.
  3. 11
  4. 8

Explanation

Multiplying every observation by a constant multiplies the standard deviation by the absolute value of that constant. Since the constant is 3, the new standard deviation is 8 × 3 = 24.

Question 40Fundamentals of Business Mathematics

A boat covers 24 km downstream in 3 hours and returns upstream in 4 hours. What is the speed of the boat in still water?

  1. 7 km/h Correct answer.
  2. 8 km/h
  3. 5 km/h
  4. 6 km/h

Explanation

Downstream speed = 24/3 = 8 km/h. Upstream speed = 24/4 = 6 km/h. The speed in still water is the average of downstream and upstream speeds: (8 + 6)/2 = 7 km/h.

Question 41Arithmetic and Algebra

A trader's sales rise from ₹48,000 to ₹60,000. What is the percentage increase in sales?

  1. 12%
  2. 30%
  3. 25% Correct answer.
  4. 20%

Explanation

Percentage increase is computed on the original value: increase = 60,000 − 48,000 = 12,000, and 12,000 ÷ 48,000 × 100 = 25%. The base for any percentage change is always the earlier (original) figure, not the new figure.

Question 42Arithmetic and Algebra

Simplify: 5(2x − 3) − 4(x − 2)

  1. 6x − 7 Correct answer.
  2. 14x − 23
  3. 6x − 23
  4. 6x + 7

Explanation

Expand each bracket: 5(2x − 3) = 10x − 15 and −4(x − 2) = −4x + 8. Combining like terms gives 10x − 4x = 6x and −15 + 8 = −7, so the result is 6x − 7.

Question 43Arithmetic and Algebra

The simple interest on ₹12,000 for 3 years at 8% per annum is:

  1. ₹960
  2. ₹3,200
  3. ₹2,880 Correct answer.
  4. ₹2,400

Explanation

Simple interest is I = P × R × T ÷ 100 = 12,000 × 8 × 3 ÷ 100 = 2,880. Simple interest is charged only on the original principal, so the annual interest of ₹960 is repeated for three years.

Question 44Arithmetic and Algebra

What is the value of 4³ ÷ 4⁵ expressed as a fraction?

  1. 1/4
  2. 1/16 Correct answer.
  3. 4²
  4. 1/8

Explanation

When dividing powers with the same base, subtract the exponents: 4^(3−5) = 4^(−2). A negative exponent gives the reciprocal, so 4^(−2) = 1/4² = 1/16.

Question 45Arithmetic and Algebra

Two numbers are in the ratio 5 : 7 and their sum is 144. What is the larger number?

  1. 60
  2. 84 Correct answer.
  3. 90
  4. 72

Explanation

The ratio parts total 5 + 7 = 12, so one part equals 144 ÷ 12 = 12. The larger number is 7 × 12 = 84, while the smaller is 5 × 12 = 60.

Question 46Arithmetic and Algebra

The arithmetic mean of five observations is 18. If one observation equal to 10 is removed, what is the mean of the remaining four?

  1. 20 Correct answer.
  2. 22
  3. 16
  4. 18

Explanation

The total of the five observations is 5 × 18 = 90. Removing 10 leaves 80 for four observations, so the new mean is 80 ÷ 4 = 20.

Question 47Arithmetic and Algebra

Solve for x: 3x − 7 = 2x + 5

  1. x = 12 Correct answer.
  2. x = 2
  3. x = 6
  4. x = −12

Explanation

Collect the x-terms on one side: 3x − 2x = 5 + 7, which gives x = 12. Substituting back, both sides equal 29, confirming the solution.

Question 48Arithmetic and Algebra

A sum becomes ₹6,600 after 2 years at 10% per annum compound interest, compounded annually. The original principal is closest to:

  1. ₹5,455 Correct answer.
  2. ₹5,280
  3. ₹5,500
  4. ₹6,000

Explanation

For compound interest, A = P(1 + r)^n, so P = 6,600 ÷ (1.10)² = 6,600 ÷ 1.21 ≈ 5,454.55, which rounds to about ₹5,455. Using simple interest would wrongly give 6,600 ÷ 1.20 = ₹5,500.

Question 49Arithmetic and Algebra

If a² − b² = 45 and a − b = 5, what is the value of a + b?

  1. 9 Correct answer.
  2. 5
  3. 40
  4. 15

Explanation

The difference of two squares factorises as a² − b² = (a + b)(a − b). Substituting gives 45 = (a + b) × 5, so a + b = 9.

Question 50Arithmetic and Algebra

A shopkeeper marks an article 40% above cost and then allows a 25% discount on the marked price. What is the profit percentage?

  1. 5% Correct answer.
  2. 10%
  3. 15%
  4. 20%

Explanation

Take cost as 100; the marked price is 140 and after a 25% discount the selling price is 140 × 0.75 = 105. Profit is therefore 5 on a cost of 100, i.e. 5%. Successive percentage changes must be multiplied, not added.