CA Foundation May 2026 Suggested Answers Paper 3 Quantitative Aptitude

FOR CA FOUNDATION EXAM PREPARATION

CA Foundation 2026
Suggested Answers ·
Paper 3 Quantitative
Aptitude
EXAM YEAR TYPE

CA Foundation 2026 Suggested Answers
SUBJECT DATE

Paper 3 Quantitative Aptitude May 2026

Notes · Sample Papers · Previous Year Papers · Mock Tests

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PAPER – 3: QUANTITATIVE APTITUDE
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All Question are compulsory.
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em& β are roots of the equations x - 2x – 35 = 0, where (α ≥ β), then glas
Time: 2 Hours Marks: 100
Ifsα
lafind the value of (α − β ) a
1. 2

a g 2

(α + β ) 2

(a) 18
(B) 24
(C) 32
(D) 36

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2. The set of inequalities 2x + 3y < 9, 5x - y > 3 has _________ region.
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(A) Unbounded solution
(B) Bounded solution
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(C) No solution
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(D) Exactly a point solution
3. The feasible region formed by linear inequalities is always a _________
region.
(A) Circular
(B) Concave

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(C) Convex

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(D) Irregular

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The system of equations
la se
las 2x + y = 10
a g
ag 4x + 6y = 36
has solution with x = _____________
(A) 2

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FOUNDATION EXAMINATION: MAY 2026

(B) 3
(C) 5
(D) 6
5. One experienced person does 10 units of work per day, while a
fresher does 5 units of work per day. The employer wants to maintain at
least 50 units of work per day. This situation can be expressed as
_____________
(A) 10x + 5y > 50 x ≥ 0, y ≤ 0
(B) 10x + 5y ≤ 50 x ≥ 0, y ≤ 0
(C) 10x + 5y ≥ 50 x ≥ 0, y ≥ 0
(D) 10x + 5y = 50 x ≥ 0, y ≤0
6. If the difference between the annually compounded interest and simple
interest on a certain sum of money at 8% per annum for 3 years is ` 788.
Then the principle amount is ______________.
(A) ` 39,175
(B) ` 39,475
(C) ` 39,975
(D) ` 40,475
7. What will be the approximate future value of an annuity of ` 1000 made
annually for 5 years at interest rate of 7% per annum, compounded
annually? (Given (1.07)5 = 1.40255)
(A) ` 8,025
(B) ` 5750
(C) ` 7,013
(D) ` 6,412
8. A machine depreciates at a rate of 10% per year on its beginning-of-year
value. If it is sold for ` 6,000 after 9 years, what was its original purchase
price?
(A) ` 14,587

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QUANTITATIVE APTITUDE

(B) ` 15,488
(C) ` 14,875
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(D) ` 15,888
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9.
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Rakesh requires ` 1,00,000 to buy a scooter after 4 years. What will
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be the approximate present value of ` 1,00,000 if the interest rate is
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10% per annum?
a g
ag (A) ` 67,800
(B) ` 68,300
(C) ` 70,935
(D) ` 71,430
10. Raju deposit ` 20,000 in a nationalized bank for 3 years at an annual
interest rate of 8%, with the interest compounded every quarter. Find

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out how much interest Raju earns in the first year and the second year.
(A) ` 1,632 & ` 1,712
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(B) ` 1,684 & ` 1,738
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(C) ` 1,648 & ` 1,784
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(D) ` 1,696 & ` 1,746 a
11. Find the effective interest rate, if nominal rate is 12% per annum,
quarterly compounding.
(A) 12%
(B) 12.36%

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(C) 12.55%

m (D) 13%
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c. o 12. Find s em
out the number of 5-digit even numbers that can be formed

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digits 1 to 7 without repetition of any digit.

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(A) 720
(B) 360
(C) 1080

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FOUNDATION EXAMINATION: MAY 2026

(D) 840
13. If the first term of a geometric progression exceeds the second term by
4 and the sum of its terms till infinity is 100, then the common ratio is
___________.
1
(A)
5
4
(B)
5
3
(C)
5
2
(D)
5
14. The sum of the first n terms of an arithmetic progression (A.P.) is
4n2 + 3n. The 10th term of the A.P. is ____________.
(A) 77
(B) 83
(C) 81
(D) 79
15. If the sum of 4th and 8th term of an arithmetic progression (A.P.) is 120,
then the 6th term of the A.P. is ____________.
(A) 10
(B) 70
(C) 60
(D) 100
1 1 1
16. The sum of infinite terms of the geometric series 1- + - +.... will
5 25 125
be ____________.
(A) 1

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5
(B)
6

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6
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(C)
5
4.c o e m
(D) m
e 5 la s
a s
l If x (m) = am , y(m) = a / m , then find the value of dy a g
ag
17. 2 2

dx
1
(A)
m2
-1
(B)
m2
1
(C)
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m4
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-1
s
(D)
m4
xg
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Calculate the integral ∫ a dx
25
18 26
x
(A) logx + C
(B) log x
(C) C
(D) 2 log x

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dy
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19. If x y = y X then = __________

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y ( x log y − y )
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(A)

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x( y log x − x)
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ag (B)
y ( x log y + y )
x( y log x − x)

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FOUNDATION EXAMINATION: MAY 2026

y ( x log y − y )
(C)
x( y log x + x)
x( x log y − y )
(D)
y ( y log x − x)
20. For a given Revenue function R(x) =100x - 2x2, the maximum
revenue occurs at x = ____________.
(A) 20
(B) 25
(C) 30
(D) 50
21. Find the next term in the series 11, 12, 14, 17, 22, 30, _____________.
(A) 42
(B) 43
(C) 38
(C) 41
22. Anil's house faces east. From the back-side of the house, he walks
straight 50 meters, then turns to the right and walks 50 meters. Finally,
he turns towards left and stops after walking 25 meters. Now, in which
direction is Anil from the starting point?
(A) South-East
(B) North-East
(C) South-West
(D) North-West
23. If A x B means A is to the south of B; A + B means A is to the north of
B; A % B means A is to the east of B; A - B means A is to the west of B;
then in P % Q + R - S, in which direction is S with respect to Q?
(A) South-West
(B) South-East
(C) North-East
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(D) North-West
24. Vishal started from his house toward west. After walking a distance 30
m
c. o
meters, he turned towards right and walk 20 meters. He then turned left
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and moved a distance of 10 meters, turned to his left again and walked

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40 meters. He now tum to left and walk 5 meters, finally he turns to left.
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In which direction he is walking now?

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ag (B) South
(A)

(C) East
(D) South-West
25. Puru started from his house towards west. After walking a distance of
25 m, he turned to the right and walked 10 m. He then again turned to
the right and walked 15 m. After this, he is to tum right at 135° and to
cover 30 m. In which direction should he go?
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(A) West
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a
(B) South

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(C) South-West
(D) South-East
26. Six students A, B, C, D, E and F are sitting in a bench facing north. C is
sitting second to the right of F. A is sitting extreme left end of the
bench. E is sitting second to the right of C. D is sitting immediate left of E.
Who is sitting between F and C?
(A) A

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(B) B
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(C) E

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27. Sharma points to a girl and says, "She is the mother of

a daughter". What is the relation of the girl with Sharma?
(A) Mother
(B) Daughter

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FOUNDATION EXAMINATION: MAY 2026

(C) Sister
(D) Daughter-in-law
28. P is the sister of Q. R is the mother of Q. S is the father of C. R is the
sister of S. T is the mother of S. What is the relation of P with T?
(A) P is Mother of T
(B) T is P's Grand Mother
(C) P is Sister of T
(D) T is Brother of P
29. Dr. Madhu said, "The engineer who is my brother is the son of the only
Professor in our family." If the Professor is Mr. Murli, how is Mr. Murli
related to Dr. Madhu?
(A) Uncle
(B) Father
(C) Brother
(D) Cousin
30. A is brother of B. P is the sister of Q. B is the son of P. How is A related
to P?
(A) Brother
(B) Son
(C) Father
(D) Uncle
31. Q's mother is the sister of P and daughter of S. A is the son of P and
Brother of H. G is the father of H. How is G related to S?
(A) Nephew
(B) Son-in-law
(C) Grandfather
(D) Father-in-law
32. Interview method is used for collection of ____________.

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(A) Primary data
(B) Secondary data
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(C)
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Discrete data
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(D)
c. o
Continuous data
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e m represents cumulative frequencies on a graph. By what other las
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33. An ogive

l aname is this graphical form commonly known?
a
ag (A) Frequency Histogram
(B) Cumulative Frequency Curve
(C) Frequency Polygon
(D) Area Diagram
34. If the mean 40, k, 6k, 4k2, 8k-4k2 is 20, then the value of k is _____________.
(A) 15
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(B) 10
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(C) 8
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(D) 4
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35. a
The standard deviation is zero only if all the observations assumed by a
variable are _____________.
(A) different
(B) equal
(C) square of natural numbers
(D) square root of natural numbers
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36. To add flexibility to the sampling process, the __________ is preferred.
.co
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s em (B) Stratified Sampling
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(C) Multi-stage Sampling
(D) Judgment Sampling

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FOUNDATION EXAMINATION: MAY 2026

37. In a sample survey, sampling error mainly arises because:
(A) Enumerators record some responses incorrectly
(B) A part of the selected sample does not respond
(C) Only a subset of the population is observed instead of a complete
census
(D) Some questions in the schedule are ambiguously worded
38. The mean of five observations is 28. Among the five observations, three
observations are 10, 23 and 62. The difference between the remaining
two observations is 13. Then the remaining two observations are _______.
(A) 30 and 17
(B) 38 and 15
(C) 29 and 16
(D) 35 and 22
39. Which of the followings is a property of Arithmetic Mean?
(A) Sum of deviations from Arithmetic Mean is always positive.
(B) Arithmetic Mean is not affected by extreme values.
(C) Sum of deviations from Arithmetic Mean is always zero.
(D) Arithmetic Mean cannot be calculated for grouped data.

x
40. The probability of getting pass in an examination is . If the probability
3
2
of getting fail is , then the value of x is ___________.
3
(A) 2
(B) 3
(C) 1
(D) 0
41. Two dice are rolled. What will be the probability that one dice have
multiple of 3 and other dice have multiple of 2?

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1
(A)
2

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1

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(B)

.
3
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m1
e 4 la s
l a s
(C)
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5
42. The mean of 10 observations is 15. If one observation 12 is replaced by
22, what will be the new mean?
(A) 16
(B) 14
(C) 17
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(D) 18
43. If ƒ(x) = kx , 0 ≤ x ≤ 1 is ase
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l k is ___________.
probability density function of a random
2

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variable x, then the value of
(A) 0
(B) 3

1
(C)
3
(D) 2

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44. In a binomial distribution, the probability of success is 0.7. The variance

m for n = 15 is ____________.
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c. o se
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(A) 4.50

s g la
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(B) 3.15

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(C) 7.35
(D) 2.10

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FOUNDATION EXAMINATION: MAY 2026

45. For a Binomial Distribution with mean = 4 and variance = 3, what are the
values of n and p?
(A) n = 16, p = 0.25
(B) n = 12, p = 1/3
(C) n = 8, p = 0.5
(D) n = 16, p = 0.75
46. The covariance between two variables X and Y is 4. The standard
deviation of X is 10 and the correlation coefficient between X and Y is
0.4. Find the standard deviation of Y.
(A) 1
(B) 2
(C) 3
(D) 4
47. The mean and mean deviation of a normal distribution are 13.5 and 4.8
respectively. Then the third quartile of the normal distribution is
_________.
(A) 6.25
(B) 17.55
(C) 4.05
(D) 1.75
48. The mean of a binomial distribution is 4 and the variance is 3.2. If
p < 0.5, find the value of p.
(A) 0.2
(B) 0.4
(C) 0.1
(D) 0.3
49. If 2x + 3y + 2 = 0 is the regression equation of x on y and the arithmetic
mean of y is -2, then arithmetic mean of x is _________.
(A) 4

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(B) 6
(C) -2
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(D) 2
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50.
c. o
A price index with base 2000 shows:
s e m
s emfor 2010: 140
Index
g la
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a What is the index for 2010 when base is shifted to 2020?
(A) 57.14
(B) 66.67
(C) 75.00
(D) 133.33
51.
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Which formula correctly represents Fisher's Price Index?

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(A) ( ∑ p1q0 / ∑ p0 q0 ) × ( ∑ p1q1 / ∑ p0 q1 ) × 100

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 

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(B) ( ∑ p1q0 / ∑ p0q0 ) × 100
1 1
a
(C) ( ∑ p q / ∑ p q ) × 100
0 1

(D) ( ∑ p0q1 / ∑ p1q0 ) ×100
 
52. If Σp0q0 = 400 and Σpnq0 = 720 and Paasche's index number is 125, then
the Fisher's index number is __________.

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(A) 125

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(D) 180

g a ` 12,500 nominal
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53. What is the approximate real wage of a worker earning
wage, when the cost of living index is 250 (base 100)?
(A) ` 3,125

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FOUNDATION EXAMINATION: MAY 2026

(B) ` 4,500
(C) ` 5,000
(D) ` 6,250

( a x ) will be ____________.
-b
54. The simplified value of 4
a6b x 4 3 -4

(A) x1+2b
(B) x2b
(C) 1
3
b
(D) a2 x b
2a+ 3b
55. If a : b = 3 : 4, then the value of
3a+ 2b
(A) 18/17
(B) 17/18
(C) 6/7
(D) 7/6
56. The product of two numbers is 7644 and their ratio is 12:13. Then, the
smaller of two numbers is __________.
(A) 91
(B) 84
(C) 82
(D) 90
log316 × log 2 3
57. The value of
log8 3 × log9 4

(A) 16
(B) 24

1
(C)
16

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1
(D)
12

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1
8 , then the value of x +
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58. If x = 3 + is

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x
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(A) m3 8
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a s
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a (C) 8
(D) 2 8
59. The compound interest for·` 15,000 at 20% per annum for 2 years
compounded semi-annually is __________.
(A) ` 9,661.50

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(B) ` 6,961.50
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(C) ` 9,691.50
(D) ` 6,696.15
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60. Mr. Amit bought a carg for ` 3,00,000 by making a down payment
a
` 50,000 and decided to pay equal annual payment for 10 years. How
much would be each payment if the interest on unpaid amount is 18%
per annum, compound annually? (Given that P(10, 0.18) = 4.49409)
(A) ` 55,628.61
(B) ` 55,266.86
(C) ` 55,555.28

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(D) ` 50,000.00
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c. o 61. The simple interest at the rate of p% per annum for p yearsm
s e will be ` p.

em Then, the principal is ____________.
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(A) ` p
(B) ` 100 p

100
(C) `
P2
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FOUNDATION EXAMINATION: MAY 2026

100
(D) `
P
62. The future value of an annuity of ` 2000 made annually for 8 years at
interest rate of 14% per annum, compound annually is _______. (Given
that (1.14)8 = 2.8526)
(A) ` 26,465.71
(B) ` 26,646.57
(C) ` 20,000.55
(D) ` 18,564.52

1
63. Ravi deposits some amount in bank for 5 years at the simple interest
2
rate of 7% per annum. Ravi receives ` 66,480 at the end of term.
Compute the amount of initial deposit by Ravi in the Bank.
(A) ` 48,000
(B) ` 50,000
(C) ` 45,000
(D) ` 51,000
64. In how many years will ` 50,000 become ` 75,000 at 8% per annum
compound interest? (Given log (1.5) = 0.1761 and log (1.08) = 0.0334)
(A) 4.8 years
(B) 5.1 years
(C) 5.3 years
(D) 5.6 years
65. If ` 50,000 grows to ` 80,525.5 in 5 years, the compound annual growth
rate (CAGR) is ___________.
(A) 9%
(B) 10%
(C) 11%
(D) 12%
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66. In how many ways 5 Indians and 5 Americans people are seated around
a table so that no two Indians are in adjacent positions?

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(A) 3! x 4!

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(C) 4!. x 5!
(B) 3! x 5!

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a
a67.g annum
A loan of ` 1,00,000 is repaid in 3 equal annual instalments at 10% per
interest, compounded annually. Find the amount of each
instalment. (Given P(3,0.1) = 2.48685)
(A) ` 41,211
(B) ` 41,311
(C) ` 39,800

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(D) ` 40,212

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68. A group consists of 7 men and 5 women. In how many ways can a group

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of 4 members be selected if the group has no women?
(A) 70
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(B) 30 a
(C) 24
(D) 35
69. Four cards are drawn at random from a standard deck of 52 playing
cards without replacement. In how many ways it can be done such that
the selected cards consist of exactly one Jack and three Aces?

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(A) 2304
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(C) 2260

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(D) 2164
a 70 In a class, 50 students have expressed that they like Mathematics, while
66 students like Accountancy. Among these, 36 students like both

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FOUNDATION EXAMINATION: MAY 2026

Mathematics and Accountancy. Based on this information, determine
how many students in the class like either Mathematics or Accountancy?
(A) 14
(B) 20
(C) 52
(D) 80
71. Relation on integers is defined by:
aRb ⇔ a - b is divisible by 5.
This relation is __________.
(A) Reflexive only
(B) Symmetric only
(C) Equivalence relation
(D) Neither symmetric nor transitive

72. Let the function ƒ : R → R is defined by ƒ(x) = x2 + 3, then ƒ −1 (12) is

(A) 3
(B) 3
(C) 9
(D) 12

x 2 +2x +2
73. Evaluate lim
x →∞ 3x 2 + x +1

1
(A) -
3

2
(B)
3

3
(C)
8
(D) 2

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74. If ‘DOCTOR’ is coded as 423527 and 'PATIENT' is coded as 8651905, then
how is 'OPERATION' coded?

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(A) 289765120

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(B) 297681205

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(C) 298765120
s g l a
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a
a75.g Ifwhat
the word 'CODE' is coded as 1357 and 'GAMER' is coded as 24678,
word does the number 84178 represent?
(A) ROVER
(B) RCEAR
(C) RACER
(D) RAECR

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76. Ram started walking 2 kms towards the Sun in the morning. He turned
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right and walked 2 kms. Then, he turned right and walked 2 kms. Finally,

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he turned left and walked 2 kms. In which direction is he walking now?
(A) South
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(B) North a
(C) East
(D) West
77. In a certain Language, 'SUBJECT' is written as 'UWDLGEV' then
'MENTION' will be written as _____________.

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(A) OGKVPQP

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se
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(D) OGPVKQP

g a ____________.
a
78. Find the next term of the series: 7, 8, 18, 57, 232, 1165,
(A) 6996
(B) 5840

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FOUNDATION EXAMINATION: MAY 2026

(C) 4672
(D) 6990
79. Five persons A, B, C, D & E are sitting on a bench. A is immediately to
the left of C. E is immediately to the left of D and right of A. D is to the
left of B. Which person is sitting in the middle of the bench?
(A) B
(B) E
(C) A
(D) D
80. Six friends A, B, C, D, E and F sit in a row facing north.
A and B have two persons between them.
C, who is at right end, is immediate right of A.
D is not neighbour of B.
E sits at left end.
Who sits third from left?
(A) F
(B) A
(C) D
(D) B
81. Six persons A, B, C, D, E, and F are seated at a round table facing outside
the centre but not necessarily in the same order. A sits at the immediate
right of E. C sits after one person to the right of A. B sits beside A and F sits
at the immediate right of D. How many persons are sitting between A & D?
(A) 1
(B) 2
(C) 3
(D) 4

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82. In a circular arrangement of 5 persons facing centre, A is sitting between
B and C, D is sitting immediate right of C, and E is sitting immediate left
of B. Who is sitting between D and B?
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(A) A

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(B)
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B
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(C)s a g
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Which one of the following parts is used to show the units of
measurement?
(A) Body
(B) Caption
(C) Box-head

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(D) Stub

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84. Data that is classified according to an attribute or characteristic of the

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items under study is referred to as ______________.
(A) Qualitative data
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(B) Chronological data a
(C) Geographical data
(D) Quantitative data
85. A researcher wants to study the effectiveness of a new treatment by
surveying the most experienced doctors in a city. He selects 50 doctors
based on their reputation and years of experience. Which type of

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sampling method is used in this survey?

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(A) Simple Random Sampling

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(B) Stratified Sampling
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86. Which of the following statement is true?
(A) Mean of the statistic is known as Standard Error

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FOUNDATION EXAMINATION: MAY 2026

(B) Mean deviation of the statistic is known as Standard Error
(C) Standard deviation of the statistic is known as Standard Error
(D) Geometric mean of the statistic is known as Standard Error
87. Mutually Exclusive classification of class intervals ____________.
(A) Excludes both the class limits
(B) Excludes the upper class limit but includes the lower class limit
(C) Includes the upper class limit but excludes the lower class limit
(D) Include both the class limits
88. The given frequency distribution is:

X 1 2 3 4 5 6 7
Y 5 9 12 17 14 10 6
The arithmetic mean of the Frequency distribution is ___________.
(A) 2.99
(B) 3.06
(C) 4.10
(D) 4.71
89. What will be the mean deviation for the numbers {2, 4, 7, 8, 9, 12} from
the mean?
(A) 2.14
(B) 2.33
(C) 2.55
(D) 2.67
90. If third quartile and first quartile are 64.5 and 22 respectively, then the
quartile deviation is
(A) 42.5
(B) 21.25
(C) 36.25

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(D) 30.5
91. The arithmetic mean (A.M.) of two positive numbers exceeds their
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harmonic mean by 30. If their A.M. is 45, Then, their geometric mean will

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be ___________.
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(A) 27
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(B)
a (C) 42
(D) 15 3
92. Two groups of students have harmonic means of 50 and 30 for their test
scores, with 10 students in the first group and 15 students in the second
group. What will be the combined harmonic mean of the two groups?
(A) 15.35
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(B) 35.71
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(C) 38.11
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(D) 42.50
93. A card is drawn at random
the probability that the card drawn is either a King or a Heart?

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(A)
52

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(B)
52

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13

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_______________.
(A) e-6

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FOUNDATION EXAMINATION: MAY 2026

(B) e-3
(C) e-9
(D) e-1
95. In a Shooting competition, A hit the target 6 out of 13 shots, and B hit 8
out of 11 shots. If they both try once, what is the probability that the
target would be hit at least once?

21
(A)
143

56
(B)
143

74
(C)
143

122
(D)
143
96. A bag contains 5 red, 4 blue, and 3 green balls. Two balls are drawn at
random without replacement. What is the probability that both balls are
of different colours?

45
(A)
66

47
(B)
66

47
(C)
132

45
(D)
132
97. For a set of observations on variables x and y, the following summary
statistics are given:

n = 5, ∑ x = 10, ∑ y = 25, ∑ xy = 70, ∑ x2 = 30 .

The regression equation of y on x is expressed as:

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y = a +bx.
What is the value of the slope b?
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(A) 0.5
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(B)
c. o
1.0
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(C) m1.5 a
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(D) 2.0

corresponding value index in __________.
(A) Time reversal test
(B) Factor reversal test
(C) Circular test
(D) Unit test
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The Spearman's Rank correlation coefficient between Economics and

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75
Accountancy marks for a class student

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is and the sum of Square of

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differences in ranks for Economics and Accountancy marks is 40. What is
the number of students in the class?
(A) 10
(B) 15
(C) 18
(D) 20

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100. When the two regression coefficients are given as bxy = 0.6 and byx = 0.9,

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determine the value of the coefficient of correlation.
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c. o (A) 0.73
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(C) 0.82
(D) 0.54

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FOUNDATION EXAMINATION: MAY 2026

ANSWERS

1. (D) 2. (A) 3. (C) 4. (B) 5. (C)
6. (C) 7. (B) 8. (B) 9. (B) 10. (C)
11. (C) 12. (C) 13. (B) 14. (D) 15. (C)
16. (B) 17. (D) 18. (A) 19. (A) 20. (B)
21. (B) 22. (D) 23.. (B) 24. (A) 25. (C)
26. (B) 27. (D) 28 (B) 29. (B) 30. (B)
31. (B) 32. (A) 33. (B) 34. (D) 35. (B)
36. (C) 37. (C) 38. (C) 39. (C) 40. (C)
41. ( )∗ 42. (A) 43. (B) 44. (B) 45. (A)
46. (A) 47. (B) 48. (A) 49. (D) 50. (B)
51. (A) 52. (C) 53. (C) 54. (A) 55. (A)
56. (B) 57. (B) 58. (B) 59. (B) 60. (A)
61. (D) 62. (A) 63. (A) 64. (C) 65. (B)
66. (C) 67. (D) 68. (D) 69. () ∗
70. (D)
71. (C) 72. (B) 73. (A) 74. (A) 75. (C)
76. (A) 77. (D) 78. (A) 79. (B) 80. (A)
81. (B) 82. (D) 83. (C) 84. (A) 85. (C)
86. (C) 87. (B) 88. (C) 89. (D) 90. (B)
91. (D) 92. (B) 93. (C) 94. (C) 95. (D)
96. (B) 97. (D) 98. (B) 99. (A) 100. (A)

∗
Q No: 41 and Q No 69: None of the options are correct

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