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Quantitative Aptitude Sample Paper - 1
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Page 1
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
Page 2
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
Page 3
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
Page 4
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
4
(c) Rs. 40,000
(d) Rs. 45,000
18. The population of a town increases every year by 2 % of the population beginning of that year. The number
of years by which the total increase of population be 40% is
(a) 7 years
(b) 10 years
(c) 17 years (approximately)
(d) none of these
19. Find the future value of an annuity of Rs. 500 made annually for 7 years at interest rate of 14 % per annum
[Given that (1.14)
7
= 2.5023]
(a) Rs. 5365.35
(b) Rs. 5000
(c) Rs. 5325.65
(d) Rs.6000.35
20. Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly .
What is the future value of this annuity after 10
th
payment? [Given that (1.005)
10
= 1.0511]
(a) Rs. 2045
(b) Rs.5055
(c) Rs.2044
(d) Rs.2065
21. Suppose your father decides to gift you Rs. 10,000 every year starting from today for the next five years, you
deposit this amount in a bank as and when you receive and get 10% per annum interest rate compounded
annually. What is the present value of this annuity? ( P(4, 0.10) = 3.16987)
(a) Rs.41,698.70
(b) Rs.45,698.70
(c) Rs.42,698.70
(d) Rs.43,698.70
22. Nominal Rate of Return =
(a) Real Rate of Return – Inflation
(b) Real Rate of Return + Inflation
(c) Inflation -Real Rate of return
(d) None of the above
23. Net Present Value (NPV)
(a) Present value of net cash Inflow – Total net Investment
(b) Present value of net cash Inflow – Present value of cash outflow
(c) Total net Investment- Present value of net cash Inflow
(d) a or b
24. The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population
will be doubled assuming there is no immigration or emigration is
(a) 35 years
© The Institute of Chartered Accountants of India
Page 5
1
FOUNDATION COURSE
MOCK TEST PAPER
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Time Allowed 2 Hours Maximum Marks: 100
QUESTIONS
PART A: BUSINESS MATHEMATICS AND LOGICAL REASONING
1. The ratio compounded of 2:3, 9:4, 5:6 and 8: 10 is
(a) 1: 1
(b) 1:5
(c) 3: 8
(d) none of these
2. The sub-triplicate ratio of 8: 27
(a) 27: 8
(b) 24: 81
(c) 2: 3
(d) none of these
3. If
p r p r
q s q s
?
??
?
, the process is called
(a) Subtrahendo
(b) Componendo
(c) Alternendo
(d) none of these
4. The value of
? ? ? ? ? ?
2 2 2 2 2 2
a ab b b bc c c ca a
a b c
b c a
x x x
x x x
? ? ? ? ? ?
? ? ? ? ? ?
??
? ? ? ? ? ?
? ? ? ? ? ?
(a) 1
(b) 0
(c) -1
(d) none of these
5. If a =
12
log 24 , b =
36
log 24 , b =
48
log 36 then prove that 1 + abc =
(a) 2bc
(b) 2ca
(c) 2ba
(d) 3bc
6. If x = 5
1/3
+ 5
-1/3
, 5x
3
-15x is given by
(a) 25
© The Institute of Chartered Accountants of India
2
(b) 26
(c) 27
(d) 30
7. Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice
that of his son. The present age of the father and the son are
(a) (50, 20)
(b) (60, 20)
(c) (55, 25)
(d) none of these
8. When two roots of quadratic equations are a and
1
?
then what will be quadratic equation.
(a) a x
2
-(a
2
+1) x + a = 0
(b) a x
2
- a
2
x + a = 0
(c) a x
2
+
(a
2
+1) x + a = 0
(d) none of these
(9) Let a and ß be the roots of equation x
2
+7 x + 12 = 0. Then the value of
22
aß
+
ßa
??
??
??
will be
(a)
49 144
144 49
+
??
??
??
(b)
7 12
12 7
+
??
??
??
(c)
91
12
??
?
??
??
(d) none of these
10. If A =
52
13
? ??
??
?
??
, then Adjoint of Matrix A
(a)
32
15
? ??
??
?
??
(b)
52
13
??
??
?
??
(c)
32
15
? ??
??
??
(d)
32
15
??
??
??
© The Institute of Chartered Accountants of India
3
11. If A =
5
0
x
y
??
??
??
and A = A
T
, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) none of these
12. If A =
23
2
ii
ii
??
??
??
(here i
2
= -1) then A =
(a) 2
(b) 8
(c) 4
(d) 5
13. On solving the inequalities 5x + y =100, x + y = 60, x = 0 and y = 0, we get the following situation.
(a) (0, 0), (20, 0), (10, 50) and (0,60)
(b) (0, 0), (60, 0), (10, 50) and (0,60)
(c) (0, 0), (20, 0), (0, 100) and (10,50)
(d) none of these
14. A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
15. A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will
get
(a) Rs. 9,000
(b) Rs.8, 800
(c) Rs. 9,200
(d) Rs. 9261
16. The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum
convertible quarterly is
(a) Rs. 240
(b) Rs. 200
(c) Rs.220
(d) Rs.210
17. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is Rs. 21870,
calculate the value of furniture 3 years ago.
(a) Rs. 30,000
(b) Rs. 35,000
© The Institute of Chartered Accountants of India
4
(c) Rs. 40,000
(d) Rs. 45,000
18. The population of a town increases every year by 2 % of the population beginning of that year. The number
of years by which the total increase of population be 40% is
(a) 7 years
(b) 10 years
(c) 17 years (approximately)
(d) none of these
19. Find the future value of an annuity of Rs. 500 made annually for 7 years at interest rate of 14 % per annum
[Given that (1.14)
7
= 2.5023]
(a) Rs. 5365.35
(b) Rs. 5000
(c) Rs. 5325.65
(d) Rs.6000.35
20. Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly .
What is the future value of this annuity after 10
th
payment? [Given that (1.005)
10
= 1.0511]
(a) Rs. 2045
(b) Rs.5055
(c) Rs.2044
(d) Rs.2065
21. Suppose your father decides to gift you Rs. 10,000 every year starting from today for the next five years, you
deposit this amount in a bank as and when you receive and get 10% per annum interest rate compounded
annually. What is the present value of this annuity? ( P(4, 0.10) = 3.16987)
(a) Rs.41,698.70
(b) Rs.45,698.70
(c) Rs.42,698.70
(d) Rs.43,698.70
22. Nominal Rate of Return =
(a) Real Rate of Return – Inflation
(b) Real Rate of Return + Inflation
(c) Inflation -Real Rate of return
(d) None of the above
23. Net Present Value (NPV)
(a) Present value of net cash Inflow – Total net Investment
(b) Present value of net cash Inflow – Present value of cash outflow
(c) Total net Investment- Present value of net cash Inflow
(d) a or b
24. The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population
will be doubled assuming there is no immigration or emigration is
(a) 35 years
© The Institute of Chartered Accountants of India
5
(b) 30 years
(c) 25 years
(d) none of these
25. Y bought Motor Bike Costing 80,000 by making down payment of Rs. 30000 and agreeing to make annual
payment for four years. How much would be each payment if the interest on unpaid amount be 14%
compounded annually. [Given P (4, 0.14) = 2.91371]
(a) Rs. 17160.25
(b) Rs. 17600.25
(c) Rs.15600.25
(d) Rs. 16600.25
26. The value of K, for which the terms 7K +3, 4K-5, 2K+10 are in A.P., is
(a) 13
(b) - 23
(c) 13
(d) 23
27. If A = {1,2,3,4} and B = {1,4,9,16,25} is a function of f is defined set A to B where f(x) = x
2
then the range of f
is
(a) {1,2,3,4}
(b) {1,4,9,16}
(c) {1,4,9,16, 25}
(d) none of these
28. If
n
P r = 336 and
n
Cr = 56, then n and r will be
(a) (3,2)
(b) (8, 3)
(c) (7, 4)
(d) none of these
29. If A = {1,2,3,4,5,6,7} and B = {2,4,6} Cardinal number of AUB
(a) 3
(b) 16
(c) 5
(d) 7
30. In how many ways the letters of the word ‘ARRANGE’ be arranged?
(a) 1,200
(b) 1,250
(c) 1,260
(d) 1,300
31. The number of ways in which 8 examination papers be arranged so that the best and worst papers never
come together.
(a) 8! - 2× 7!
© The Institute of Chartered Accountants of India
Read MoreFAQs on Quantitative Aptitude Sample Paper - 1
| 1. How do I solve time and work problems in CA Foundation quantitative aptitude? |  |
Ans. Time and work problems involve calculating how long tasks take when multiple people work together. Find the work rate (portion completed per unit time) for each person, add rates for combined work, then use the formula: Time = Total Work ÷ Combined Rate. Practice with varying difficulty levels through sample papers to master different scenarios and avoid calculation errors during exams.
| 2. What's the trick to getting ratio and proportion questions right in quantitative aptitude exams? | |
Ans. The key is identifying whether quantities are directly or inversely proportional before setting up equations. Use the unitary method: find the value of one unit first, then scale to required amounts. Common mistakes include confusing proportion types and incorrect cross-multiplication. Work through past year papers to recognise patterns and strengthen speed during mock tests for CA Foundation.
| 3. Why do I keep making mistakes in percentage and profit-loss calculations? | |
Ans. Most errors stem from incorrectly identifying the base value for percentage calculations-always determine what 100% represents. For profit-loss, use formulas: Profit = Selling Price - Cost Price, and Profit% = (Profit ÷ Cost Price) × 100. Practice sample paper questions repeatedly, focusing on multi-step problems where percentages compound, to build accuracy and confidence for your exam.
| 4. How should I approach average and mixture problems in CA Foundation quantitative aptitude? | |
Ans. Average problems require finding the sum of values and dividing by count; use weighted averages when items have different frequencies. For mixture problems, apply the alligation method to find proportions of components. Sample papers demonstrate how these concepts combine in real exam scenarios. Practise both simple and complex variations to recognise question patterns and solve efficiently under timed conditions.
| 5. What's the fastest way to solve number series and pattern recognition questions? | |
Ans. Identify the relationship between consecutive terms first-check for arithmetic progressions, geometric progressions, or custom patterns involving operations like squaring or factorial sequences. Write out differences or ratios between terms to spot the rule quickly. Regular practice with mock tests and past year papers trains your pattern recognition ability, helping you solve these questions in seconds rather than minutes during your CA Foundation exam.
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