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Free CA Quantitative Aptitude Practice Questions & Answers
500 exam-style Quantitative Aptitude questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 151
The ratio of the ages of A and B is 4 : 5. After 6 years the ratio will be 6 : 7. A's present age is:
Select an option first.
Correct answer: C — 12 years
Explanation: Let the ages be 4x and 5x. Then (4x + 6)/(5x + 6) = 6/7, so 28x + 42 = 30x + 36, giving 2x = 6 and x = 3. A is 4 x 3 = 12 years old. Check: in 6 years they are 18 and 21, which is 6 : 7. Add the SAME number of years to both ages - a ratio does not age at the same rate as the people in it.
Question 152
The ratio of two numbers is 5 : 8. When 9 is added to each, the ratio becomes 8 : 11. The smaller number is:
Select an option first.
Correct answer: C — 15
Explanation: Let the numbers be 5x and 8x. Then (5x + 9)/(8x + 9) = 8/11, so 55x + 99 = 64x + 72, giving 9x = 27 and x = 3. The smaller number is 5 x 3 = 15. Check by substitution: 15 and 24 become 24 and 33, which is 8 : 11. In an objective paper with negative marking, that back-check costs seconds and prevents a wrong tick.
Question 153
Two numbers are in the ratio 3 : 5. When each is increased by 10, the ratio becomes 5 : 7. The numbers are:
Select an option first.
Correct answer: C — 15 and 25
Explanation: Let the numbers be 3x and 5x. Then (3x + 10)/(5x + 10) = 5/7, so 21x + 70 = 25x + 50, giving 4x = 20 and x = 5. The numbers are 15 and 25. Check: 25 and 35 is indeed 5 : 7. Represent the pair with a single unknown multiplier - trying two separate unknowns needs a second equation you do not have.
Question 154
If A : B = 3 : 4 and B : C = 6 : 7, then A : B : C is:
Select an option first.
Correct answer: A — 9 : 12 : 14
Explanation: Make B common. A : B = 3 : 4 = 9 : 12 (multiply by 3); B : C = 6 : 7 = 12 : 14 (multiply by 2). Hence A : B : C = 9 : 12 : 14. The technique is to scale each ratio so the shared term matches - here the LCM of 4 and 6 is 12. Distractor B simply strings the outer terms together, which is the error the question is set to catch.
Question 155
If 15% of A equals 20% of B, then A : B is:
Select an option first.
Correct answer: B — 4 : 3
Explanation: From 0.15A = 0.20B, A/B = 0.20/0.15 = 4/3, so A : B = 4 : 3. Note that the ratio comes out INVERTED relative to the percentages, which is the trap distractor C is built on: the quantity carrying the smaller percentage must be the larger, since the two products are equal.
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Question 156
If A : B = 3 : 4 and A + B = 63, then B is:
Select an option first.
Correct answer: C — 36
Explanation: The ratio terms total 7, so B takes 4/7 of 63 = 36 and A takes 27. Always convert the ratio into fractions of the whole before applying it to the total. Check that the two parts add back to 63, which distinguishes the answer from distractor A, the value of A.
Question 157
If the roots of ax squared + bx + c = 0 are reciprocals of each other, then:
Select an option first.
Correct answer: D — a = c
Explanation: If the roots are t and 1/t, their product is 1. Since the product equals c/a, we need c/a = 1, that is a = c. The sum of the roots imposes no condition, so b is unrestricted. Working from the sum and product relations answers the whole family of 'roots are related in such a way' questions.
Question 158
An asset costing Rs.2,00,000 is depreciated at 20% per annum on the reducing balance. Its book value at the end of 3 years is:
Select an option first.
Correct answer: B — Rs.1,02,400
Explanation: Each year 80% of the opening value remains, so the closing value is 2,00,000 x (0.8) cubed = 2,00,000 x 0.512 = Rs.1,02,400. Distractor A applies 20% of cost for three years, which is the straight line result. Under the reducing balance method the book value never reaches zero, however long the asset is held.
Question 159
A sum doubles itself in 5 years under compound interest. In 15 years it will become:
Select an option first.
Correct answer: B — 8 times
Explanation: Fifteen years is three doubling periods, so the sum doubles three times over: 2 x 2 x 2 = 8 times. Distractor A multiplies the doubling by the number of periods, which is the simple interest way of thinking - under compounding the growth is multiplicative, not additive.
Question 160
If one root of x^2 + kx + 12 = 0 is 3, the other root is:
Select an option first.
Correct answer: D — 4
Explanation: The product of the roots equals the constant term divided by the coefficient of x squared, that is 12. Since one root is 3, the other must be 12/3 = 4. The value of k is not needed at all, though it works out to -7. Using the product or sum relation is far quicker than substituting to find k and then solving the quadratic.
Question 161
At 8% per annum compound interest, a sum will approximately double in:
Select an option first.
Correct answer: A — 9 years
Explanation: The rule of 72 estimates the doubling period as 72 divided by the rate, so 72/8 = 9 years. The exact figure from logarithms is log 2 / log 1.08 = 9.006 years, so the approximation is very close in the range of rates met in practice. It is a useful check on any compound interest answer that claims a doubling.
Question 162
The second derivative of y = x to the power 4 is:
Select an option first.
Correct answer: B — 12x squared
Explanation: Differentiating once gives 4x cubed; differentiating again gives 12x squared. Distractor A stops after the first derivative and distractor C goes one step too far to the third. The second derivative is what determines whether a turning point is a maximum or a minimum, which is why it is examined alongside optimisation.
Question 163
Two projects have identical total cash inflows, but Project X receives more of its money in the EARLY years. At a positive discount rate:
Select an option first.
Correct answer: D — Project X has the higher net present value
Explanation: Earlier receipts are discounted by a smaller factor, so they contribute more to present value. With equal totals and equal outlays, the project with the front-loaded pattern wins. This is why the timing of cash flows matters as much as their size in investment appraisal.
Question 164
In a class of 60 students, 32 play cricket, 24 play football and 10 play both. The number who play neither game is:
Select an option first.
Correct answer: D — 14
Explanation: By the addition rule, the number playing at least one game = 32 + 24 - 10 = 46, so those playing neither = 60 - 46 = 14. Subtracting the overlap once is essential, since the 10 who play both were counted in each of the two figures. Distractor C is the number playing at least one game, offered to catch a misread of the question.
Question 165
If a set A has 4 elements, the number of subsets of A is:
Select an option first.
Correct answer: D — 16
Explanation: Each element is either included or excluded, giving 2^4 = 16 subsets, which includes the empty set and A itself. Distractor B, 15, is the number of PROPER subsets - those excluding A itself. Read the wording carefully: subsets, proper subsets and non-empty subsets give three different counts from the same set.
Question 166
The difference between compound interest, compounded annually, and simple interest on a certain sum for 2 years at 10% per annum is Rs.20. The sum is:
Select an option first.
Correct answer: B — Rs.2,000
Explanation: For two years the difference equals P(r/100)^2 = P x 0.01, so P = 20/0.01 = Rs.2,000. Check: SI = Rs.400 while CI = 2,000 x 1.21 - 2,000 = Rs.420, a difference of Rs.20. The reason for the formula is that the extra amount under compounding is simply the interest earned on the first year's interest.
Question 167
Simple interest on Rs.15,000 for 2 years and 6 months at 8% per annum is:
Select an option first.
Correct answer: D — Rs.3,000
Explanation: Convert the period to years: 2 years 6 months is 2.5 years. Interest = 15,000 x 0.08 x 2.5 = Rs.3,000. Distractor A treats the period as 2 years and distractor B as 3 years. Under simple interest the yearly charge is constant, so a part period is simply pro-rated - unlike compound interest, where it is not.
Question 168
The simple interest on Rs.2,500 at 4% per annum for 5 years is:
Select an option first.
Correct answer: B — Rs.500
Explanation: Interest = 2,500 x 0.04 x 5 = Rs.500. Under simple interest the yearly charge is a constant Rs.100, so five years give Rs.500 - and the amount repayable would be Rs.3,000. Distractor D is the interest for a single year.
Question 169
The number of ways in which the letters of the word EXAM can be arranged is:
Select an option first.
Correct answer: D — 24
Explanation: All four letters are distinct, so the count is 4! = 4 x 3 x 2 x 1 = 24. No division is needed because nothing repeats - contrast a word such as ACCOUNT, where a repeated letter requires division by the factorial of the repetition. Always check for repeated letters before applying the factorial.
Question 170
Three pens and four books cost Rs.620, while five pens and two books cost Rs.450. The cost of one book is:
Select an option first.
Correct answer: A — Rs.125
Explanation: Let p and b be the prices. 3p + 4b = 620 and 5p + 2b = 450. Doubling the second gives 10p + 4b = 900; subtracting the first leaves 7p = 280, so p = 40 and then b = (620 - 120)/4 = Rs.125. Distractor C is the price of the PEN - in an objective paper, always re-read which quantity was asked for before ticking.
Question 171
If 2x + y = 11 and x + 2y = 13, then x + y equals:
Select an option first.
Correct answer: A — 8
Explanation: Adding the two equations gives 3x + 3y = 24, so x + y = 8 - without ever solving for x and y separately. When a symmetric expression such as x + y or x - y is asked for, adding or subtracting the equations usually reaches it in one step. For the record, x = 3 and y = 5.
Question 172
To accumulate Rs.5,00,000 in 4 years at 10% per annum, the future value annuity factor being 4.641, the annual deposit required is:
Select an option first.
Correct answer: A — Rs.1,07,735
Explanation: Annual deposit = target amount / future value annuity factor = 5,00,000 / 4.641 = Rs.1,07,735. Distractor B ignores interest and simply divides by 4, and the true answer must be LESS than that because the earlier deposits earn interest. A sinking fund is used to accumulate for redemption of debentures or replacement of an asset.
Question 173
A machine costing Rs.60,000 has a scrap value of Rs.5,000 after 10 years. Under the sinking fund method at 8%, the future value annuity factor being 14.487, the annual provision is:
Select an option first.
Correct answer: D — Rs.3,796.51
Explanation: The fund must accumulate the amount needed for replacement, that is cost less scrap value: 60,000 - 5,000 = Rs.55,000. The annual provision is 55,000 / 14.487 = Rs.3,796.51. Distractor A ignores interest and simply divides by 10 - the true provision must be lower, because the earlier instalments earn interest.
Question 174
If the first derivative of a function is negative over an interval, the function is:
Select an option first.
Correct answer: B — Decreasing over that interval
Explanation: The first derivative is the rate of change, so a negative value means the function falls as x rises. A positive derivative means it rises and a zero derivative marks a stationary point. This sign test is what identifies increasing and decreasing ranges before the second derivative classifies any turning point.
Question 175
The roots of x squared - 7x + 12 = 0 are:
Select an option first.
Correct answer: C — 3 and 4
Explanation: Find two numbers with a product of 12 and a sum of 7: they are 3 and 4, so the equation factorises as (x - 3)(x - 4) = 0. Both roots are positive because the product is positive and the sum is positive. Distractor B has the right product but the wrong sum - always check both conditions, not just one.
Question 176
If the number of combinations of n things taken 2 at a time is 28, then n is:
Select an option first.
Correct answer: D — 8
Explanation: C(n,2) = n(n - 1)/2 = 28 gives n(n - 1) = 56, so n squared - n - 56 = 0 and n = 8 (the negative root is rejected). Recognising 56 as 8 x 7 solves it by inspection. Reject the negative root explicitly in a written answer - the count of objects cannot be negative, and stating why earns the mark.
Question 177
If x lies strictly between -3 and 4, then x squared lies in the range:
Select an option first.
Correct answer: D — x squared is at least 0 and less than 16
Explanation: Squaring is not monotonic across zero. The smallest value of x squared is 0, attained at x = 0, and the largest approaches 16 as x approaches 4. So x squared lies from 0 up to but not including 16. A square can never be negative, which disposes of distractor B at once.
Question 178
If A is a subset of B, then A intersection B equals:
Select an option first.
Correct answer: A — A
Explanation: Every element of A already lies in B, so the elements common to both sets are exactly the elements of A. For the same reason A union B equals B. These two identities are the standard test of whether a candidate has understood the subset relation rather than merely memorised the addition rule.
Question 179
If x = 2 and y = 3, the value of (x raised to the power y) multiplied by (y raised to the power x) is:
Select an option first.
Correct answer: B — 72
Explanation: x to the power y is 2 cubed = 8, and y to the power x is 3 squared = 9, so the product is 72. The two exponents are NOT interchangeable - 2 cubed is 8 while 3 squared is 9 - which is exactly what the question is testing. Substitute into each factor separately before multiplying.
Question 180
The product of the roots of 3x^2 - 12x + 7 = 0 is:
Select an option first.
Correct answer: C — 7/3
Explanation: For ax^2 + bx + c = 0 the sum of the roots is -b/a and the product is c/a. Here the product is 7/3 (and the sum, offered as distractor A, is 12/3 = 4). Note the sign convention: the sum carries a minus sign while the product does not, which is the point at which most errors occur.
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