CA Foundation Quantitative Aptitude MTP April 2025: Question Paper and Solutions

How to Prepare for CA Foundation Quantitative Aptitude

Solving past MTPs, RTPs, and suggested answers from previous examination windows is essential to mastering time management under the time limit applicable to your exam paper. Review step-by-step working notes, legal case precedents, and accounting disclosures with instant 24/7 AI tutor assistance via CApex.

Question directory and available solutions

200 indexed questions. Open a question to read its full statement and available answer.

1. The mean proportional to 8 and 32 is -
2. If x: y =7:8, then for 6x+5y:4x+3y =
3. If x 3 -1= 1330 and y 3 -1= 1727, then the value of x 2 -y 2 is
4. The value of 7 log (16/15) + 5 log (25/24) + 3 log (81/80) =
5. Simplification of x m+3n .x 4m-9n / x 6m-6n is:
6. Find the value of [log 10 √25 – log 10 (2 3 ) + log 10 (4) 2 ]
7. log 4 (x 2 + x) – log 4 (x+1) = 2. Find x
8. A manufacturer produces two products A and B. The profit on product A is ₹ 10 on each unit and profit on product B is ₹ 13 on each unit. Then the…
9. If (2 + √3) is a root of a quadratic equation x 2 + px + q = 0 then find the value of p and q.
10. A company produce two type of product A & B which require processing in two machines. First machine can be used up to 15 hours and second can be…
11. A certain amount at a rate of simple interest x, doubles in 5 years. At another rate of simple interest y, it becomes three time 'in 8 years. Then…
12. Anil deposited a certain amount in a bank at the rate of 10% per annum compounded semi-annually. At end of one year Anil received a sum of ₹ 13,230.…
13. The effective rate of interest corresponding to a nominal rate of 8% per annum payable quarterly is (Given that (1.02) 4 = 1.08243216)
14. If Sum triples in 15 years at Simple rate of interest, rate of interest per annum will be:
15. The future value of an annuity of ₹ 7,200 made annually for 5 years at the rate of 12% compounded annually is (Given that (1.12) 5 = 1.76234)
16. Rakesh borrows a loan of ₹10,000 from bank and he agreed to pay back in 24 equal instalments at the rate of 10% compound interest per annum. Then…
17. What is the present value of ₹ 80,000 to be required after 10 years if the interest rate be 6%? (Given that (1.06) 10 = 1.7908)
18. Sam invested ₹12,000 for 10 years in financial company. At the end of 10 th year his investment value is ₹ 18,000. Then the Compound Annual Growth…
19. Mr. A invested ₹20,000 in a bank at the rate of 4.5% p.a. He received ₹ 27,500 after end of term. Find out the period?
20. ₹1,500 is paid every years for 10 years to pay a loan. What is the loan amount, if rate of interest 5% p.a. ? If (1.05) 10 = 1.6288
21. A certain amount is invested in a bank. What annual rate of interest compounded annually becomes 8 times of this investment in 5 years? (Given that…
22. If the compound interest on a certain sum for 2 years at 5% per annum is ₹ 246, then the simple interest on the same sum for double the time and…
23. Madhu deposits ₹ 100 in a Bank at the beginning of every year for 20 years at 10% interest rate compounded annually, how much would she earn after…
24. How much amount is required to be invested every year so as to accumulate ₹ 15,00,000 at the end of 20 years if interest is compounded annually at…
25. Assuming that the discount rate is 12% per annum, how much would you pay to receive ₹100, growing at 8% annually forever?
26. In how many ways can 5 Engineers, 4 Professors, and 6 Auditors be seated in a row so that all person of the same profession sit together?
27. n articles are arranged in such a way that 2 particular articles never come together. The number of such arrangements is
28. The number of ways the letters of the word 'TRIANGLE' to be arranged so that the word 'angle' will be always present is
29. 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladiessit together. The number of ways is
30. The number of ways in which the letters of the word `MOBILE' be arranged so that consonantsalways occupy the odd places is
31. The 4 arithmetic means between -2 and 23 are
32. The first and the last terms of an AP series -8, -6, -4, ...... is 52. The number of terms is
33. The sum of 3 numbers of a G P is 39 and their product is 729. The numbers are -
34. The function f(x) = 2 x is
35. A town has a total population of 50,000. Out of it 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of…
36. If f(x) = x+3, g(x) = x 2 , then fog (x)
37. Lim n→∞ ( 1 / 3 + 1 / 3 2 + 1 / 3 3 + ...... + 1 / 3 n ) is equal to :
38. Given x = 2t + 5; y = t 2 -2, then dy / dx is calculated as:
39. If f(x) = x k and f ` (1) = 10 then the value of k is
40. The marginal revenue function for a product MR = 5-4x + 3x 2 . Then the total revenue function is -
41. Find the missing term CEGI, XVTR, GIKM, _____
42. In certain code language ‘CLOCK' is coded as 75276 and ‘EARTH' is coded as 83491, then 'COAT' is coded as
43. In a certain language ‘MENTION' is written as ‘NFOUJPO', the code of ‘MYSTIFY' is:
44. Find odd man out of the series 121, 143, 165, 186, 209
45. In a certain language, FLOWER is coded UOLDVI, then how is TERMINAL coded in that language?
46. Anil started walking 5 kms towards north then he turned left and walked 3 kms. Again, he turned left and walked 5 kms. Then the total number of kms…
47. Raju started walking 10 kms towards east from his home. He turned right and walked 5 kms to the south to reach his school. In which directions is…
48. A started walking from his house & walk 4 km north side then turns right & walk 3 km. If he turns right again, what is the direction now?
49. A man starts walking 10 km to the North. He turns right and walks 5 km, then turns right again and walks 10 km. In which direction is man now from…
50. Pointing to a lady, a man said, “The son of her only brother is the brother of my wife”. How is lady is related to man?
51. A family has a man, his wife, their four sons and their wives. The family of every son also 3 sons and one daughter. Find out the total number of…
52. Five persons A, B, C, D and E are sitting in a circle facing centre. C is sitting immediate left of E. A is sitting in between and D. Who is sitting…
53. Five people A, B, C, D, E are seated about a round table facing outside the centre but not necessary in the same order. A sits at immediate right of…
54. Five friends A, B, C, D and E are sitting in a row facing east. A is sitting between C & D. B is second to the left C. Who is sitting at the south…
55. Five persons A, B, C, D & E sitting on a bench. A is immediate right of B. E is immediate left of C and immediate right of A. B is the right of D.…
56. Given that 1. A is mother of B. 2. C is son of A. 3. D is brother of E. 4. E is daughter of B. The grandmother of D is -
57. Read the following information and answer the question 'A+B' means 'A is the daughter of B'. 'A ×B' means 'A is the son of B'. 'A - B' means…
58. B is daughter of A. C is brother of B. C is the only son of D. C and E are married couple. F is the only son of E. Then how is F related to A?
59. Give that X is mother of Y. Z is son of X. A is brother of B.B is daughter of Y. Who is grandmother of A?
60. L is wife of N, P is son of N, K is brother of N and father of O. What is the relationship of P and O?
61. Standard Error (SE) and square root of sample size are
62. The mean of three numbers is 135. Among the three numbers the biggest number is 180. The difference between the remaining two numbers is 25. Then…
63. Out of 1000 persons 40% are female, others are male. In a marriage function, 300 persons enjoyed the song.30% of the people who had not enjoyed the…
64. In tabular presentation of data, stub is
65. For open-end classification, which of the following is the best measure of central tendency?
66. In case of an even number of observations which of the following is median?
67. Non-probability Sampling is also known as:
68. Two variables x and y are given by y= 2x – 3. If the median of x is 20, what is the median of y?
69. If the relationship between two variables u and v are given by 2u + v + 7 = 0 and if the AM of u is 10, then the AM of v is
70. The appropriate measure of dispersion for open-end classification is
71. If R x and R y denote ranges of x and y respectively where x and y are related by 3x+2y+10=0, what would be the relation between x and y?
72. If x and y are related by 2x+3y+4 = 0 and SD of x is 9, then SD of y is
73. The quartiles of a variable are 45, 52 and 75 respectively. Its quartile deviation is
74. If x and y are related as 3x+4y = 20 and the quartile deviation of x is 16, then the quartile deviation of y is
75. If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10respectively, then the coefficient of variation of y is
76. What is spurious correlation?
77. When r = 1, all the points in a scatter diagram would lie
78. If the coefficient of correlation between two variables is 0.8 then the percentage of variation unaccounted for is
79. If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation…
80. If the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is -0.6, then what is the correlation coefficient…
81. What is the probability of occurrence of leap year having 53 Sunday?
82. What is the chance of picking a spade or an ace not of spade from a pack of 52cards?
83. Find the probability that a four-digit number comprising the digits 2, 5, 6 and 7 would be divisible by 4.
84. The probability that an Accountant's job applicant has a B. Com. Degree is 0.85, that he is a CA is 0.30 and that he is both B. Com. and CA is 0.25…
85. Rupesh is known to hit a target in 5 out of 9 shots whereas David is known to hit the same target in 6 out of 11 shots. What is the probability that…
86. In connection with a random experiment, it is found that P(A) = 2 / 3 , P(B) = 3 / 5 and P(A∪B) = 5 / 6 , find P(A'/B)
87. In a business venture, a man can make a profit of ₹ 50,000 or incur a loss of ₹ 20,000. The probabilities of making profit or incurring loss, from…
88. Find the probability of a success for the binomial distribution satisfying the following relation 4 P (x = 4) = P (x = 2) and having the parameter n…
89. An experiment succeeds thrice as after it fails. If the experiment is repeated 5times, what is the probability of having no success at all?
90. If the two quartiles of a normal distribution are 47.30 and 52.70 respectively, what is the mode of the distribution? Also find the mean deviation…
91. X follows normal distribution with mean as 50 and variance as 100. What is P(x≥ 60)? [GivenΦ(1) = 0.8413]
92. Number of misprints per page of a thick book follows
93. If for a Poisson variable X, f(2) = 3 f(4), what is the variance of X?
94. If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean is
95. Fisher's index number satisfies the ______ tests
96. Fisher's ideal index number is
97. if r = 0.6 then coefficient of non-determination is
98. The Cost-of-Living Index (CLI) is always
99. The Paasches and Fishers index numbers are 169 and 156 respectively, then Laspyre's Index number is
100. The whole sale price index number or agricultural commodities in a given region at a given date is 280. The percentage increase in prices of…
101. The ratio of the number of boys to the number of girls in a school of 720 students is 3: 5. If 18 new girls are admitted in the school, find how…
102. If p: q = r: s, implies q: p = s: r, then the process is called
103. If a:b = 4:5, find the value of (5a-3b): (6a + 3b)
104. The value of (243) 1/5 × (128) 1/7 is
105. The value of log x (0.00001) = – 5, then x is
106. If logx = log5 + 2 log 3 – 1 / 2 log25, then value of x is
107. If (4) 3 × (√2) 2n = 2 n , then n is
108. The point of intersection between the straight lines 3x + 2y = 6 and 3x – y = 12 lie in
109. The sum of the digits of a two digit number is 10. If 18 be subtracted from it, the digits in the resulting number will be equal. The number is
110. Solve for x, 4 x - 3.2 x+2 + 2 5 =0
111. The value of √(2 + √(2 + √(2+ ...... ∞))) is equal to
112. The values of x for the equation x 2 + 9x + 18 = 6 - 4x are
113. A dealer has only ₹5760 to invest in fans (x) and sewing machines (y). The cost per unit of fan and sewing machine is ₹360 and ₹240 respectively.…
114. The difference between Compound Interest and Simple Interest on a certain sum for 2 years at 6% p.a. is ₹ 13.50. Find the sum
115. Sequence of periodic payments/ receipts regularly over a period of time is called
116. A machine for which the useful life is estimated to be 5 years, Cost ₹ 5000 and Rate of depreciation is 10% p.a. The scrap value at the end of its…
117. If A = ₹ 1000, n = 2 years, R = 6% p.a. compound interest payable half-yearly then principal (P) is.
118. The difference between compound and simple interest at 5% per annum for 4 years on ₹ 20000 is
119. Find the future value of an annuity of ₹ 500 is made annually for 7 years at interest rate of 14% compounded annually. Given that (1.14) 7 = 2.5023.
120. The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is
121. What will be the final value of investment for the principal value of ₹ 80,000 for 4 year @10% p.a. rate of interest?
122. Find the present value of ₹ 500 due 10 years hence when interest of 10% is compounded half yearly?
123. If the value of a car gets depreciated by 20% per year, estimated value at the end of five year is _____, if its present value is ₹ 24,000.
124. A person opened a savings bank account 4 months ago, which has now a balance of ₹ 21,315. If the bank pays 4.5% simple interest, how much money was…
125. Find the present value of an annuity of ₹ 1,000 payable at the end of each year for 10 years, if the money is worth 5% effective.
126. If six times the number permutations of n things taken 3 at a time is equal to seven times the number of permutations of (n − 1) things taken…
127. In how many different ways can five persons stand in a line for a group photograph?
128. There are 5 speakers A, B, C, D and E. The number of ways in which A will speak always before B is
129. In ways can 4 Americans and 4 English men be seated at a round table so that no 2 Americans may be together?
130. The ways of selecting 4 letters from the word EXAMINATION is
131. The 7 th term of the series 6, 12, 24...... n th term is
132. The last term of the series x 2 , x, 1, .... to 31 terms is
133. If the A.M. and G.M. for two numbers are 6.50 and 6 respectively then the two numbers are
134. Let f(x) = x²-6x+9 / x-3 , x ≠ 3, f(3) = 0, then f(x) is
135. Find fo g for the functions f (x) = x 8 , g(x) = 2x 2 +1
136. If f (x) = 1 / x , f ( 1 / 2 ) is
137. If f(x) = x 2 +2, then the given function is
138. Evaluate ∫ 0 1 (2x 2 - x 3 ) dx and the value is
139. If y = e √2x , dy / dx is calculated as
140. Find dy / dx when y = 4x 3 + 8x 7 at x 2 = 2
141. If PAINT is coded as 74128 and EECEL is coded as 93596, how is ACCEPT is coded
142. If each of the letters assigned an even numeric value A= 2, B= 4 and so on, what will be the total value of the letters for the word INDIA ?
143. Find next letter series BMO, EOQ, HQS, _?
144. Find next series 8,13, 18, 23, ?, 33, 38
145. Find missing term of the next series 7, 12, 22,37, ?, 82,112, 147
146. Shobha is the niece of Ashish. Ashish's mother is Priya. Kamla is Priya's mother. Kamla's husband is Hari. Krishna is the mother-in-law of Hari. How…
147. Pointing to a boy in a photograph, Neena said, "He is the son of my grandmother's only daughter". How is Neena related to the boy?
148. Rampal told Arjun, "Yesterday I defeated the only brother of the daughter of my grandmother." Whom did Rampal defeat?
149. A# B means ‘A is the brother of B' A @ B means 'A is the daughter of B' A & B means 'A is the husband of B' A % B means 'A is the wife of B' If…
150. A is son of C while C and Q are the sisters to one another. Z is the mother of Q. If P is the son of Z, Which one of the following statements is…
151. Kailash faces towards north. Turning to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to…
152. Asha moved a distance of 75 metres towards the north. She then turned to the left and walking for about 25 metres, turned left again and walked 80…
153. Maya starts from point T, walks straight to point U, which is 4 ft away. She turns left at 90° and walks to W, which is 4 ft away, turns 90°…
154. P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre: P is second to the right of T who is the neighbour of R and V. S…
155. If North-East is called East, North is called North-East and North-West is called North, then what will south be called as?
156. Who among following is to the immediate left of F?
157. How many persons are seated between K and F?
158. Who among the following are three lady members?
159. In an Exhibition seven cars of different companies - Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo are standing facing to east in…
160. Which of the following statement is correct?
161. When the data are classified in respect of successive time points, they are known as
162. The following data relate to the incomes of 86 persons: What is the percentage of persons earning more than ₹ 1500? Income in ₹ | No. of persons…
163. Bivariate Data are the data collected for
164. _______ is the upper part of the table, describing the columns and sub columns.
165. If from a population with 25 members, a random sample without replacement of 2 members is taken, the number of all such samples is
166. Standard error can be described as
167. Which of the following measures of central tendency is based on only 50% of the central values?
168. The median of the following items, 6, 10, 4, 3, 9 11, 22, 18 is
169. For a moderately skewed distribution, which of the following relationship holds?
170. The mean salary for a group of 40 female workers is ₹ 5200 per month and that for a group of 60 male workers is ₹ 6800 per month. What is the…
171. The quartile deviation of a normal distribution with mean 10 and standard deviation 4 is
172. What is the coefficient of range for the following wages of 8 workers? ₹ 80, ₹ 65, ₹ 90, ₹ 60, ₹ 75, ₹ 70, ₹ 72, ₹ 85.
173. The third decile for the numbers 15, 10, 20, 25, 18, 11, 9, 12 is
174. The coefficient of mean deviation about mean for the first 9 natural numbers is
175. The median of 27,30,26,44,42,51,37 is
176. The mean weight for a group of 40 female students is 42 kg and that for a group of 60 male students is 52 kg. What is the combined mean weight?
177. If the relationship between x and y is given by 4x– 6y =13 and if the median of x is 16. Find median of y.
178. If the quartile deviation of x is 8 and 3x + 6y = 20, then the quartile deviation of y is
179. Find D 6 for the following observations: 7,9,5,4,10,15,14,18,6,20
180. The theory of the compound probability states that for any two events A and B:
181. The odds are 9:5 against a person who is 50 years living till he is 70 and 8:6 against a person who is 60 living till he is 80. Find the probability…
182. The probability that a trainee will remain with a company is 0.8. The probability that an employee earns more than ₹ 20,000 per month is 0.4. The…
183. If x be the sum of two numbers obtained when two die are thrown simultaneously then P (x ≥ 7) is
184. The A.M. between two numbers is 34 and their G.M. is 16, the numbers are?
185. The probability that a card drawn at random from the pack of playing cards may be either a queen or an ace is
186. If the probability of a horse A winning a race is 1 / 6 and the probability of a horse B winning the same race is 1 / 4 , ______ is the probability…
187. What is the chance of picking a heart or a queen not of heart from a pack of 52 cards?
188. A class consists of 10 boys and 20 girls of which half the boys and half the girls have blue eyes. Find the probability that a student chosen random…
189. Variance of a binomial distribution is always ______ its mean.
190. The interval (μ - 3ð, μ + 3ð) covers:
191. A manufacture, who produces medicine bottles, finds that 0.1% of the bottles are defective. The bottles are packed in boxes containing 500 bottles.…
192. For binomial distribution E(x) = 2, V (x) = 4 / 3 . Find the value of n.
193. If Standard deviation of a poisson distribution is 2, then its
194. In a normal distribution quartile deviation is 6, the standard deviation will be
195. Suppose a business executive was earning ₹ 2,050 in the base period. What should be his salary in the current period if his standard of living is to…
196. Bowley's index number is expressed in terms of:
197. In the data group Bowley's and Laspeyre's Index number is as follows. Bowley's Index number = 150, Lapeyre's Index number = 180 then Paesche's Index…
198. Consumer price index is commonly known as
199. What is the formula for calculating the detailed value?
200. The simple index number for the Current year using simple aggregative method for the following data is Commodity Year Prices (P 0 ) Current Year…