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Quantitative Aptitude (Mathematics)

Q.1: A sum of ₹ x is divided among A, B and C such that the ratio of the shares of A and C is 8 : 7 and that of B and C is 3 : 2. If the difference between the shares of A and B is ₹ 240, then what is the value of x ?
(A) 2544
(B) 2580
(C) 2490
(D) 2448

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Ans : (D) 2448

Q.2: If a pair of shoes marked at ₹350 is offered at ₹308, then what will be the discount percentage?
(A) 42%
(B) 13.6%
(C) 12%
(D) 14%

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Ans : (C) 12%

Q.3: In $\triangle ABC,$ AD is the bisector of $\angle A$ meeting BC at D, If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC, then the length of AC is:
(A) 18.5 cm
(B) 18 cm
(C) 16 cm
(D) 22.5 cm

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Ans : (D) 22.5 cm

Q.4: Simplify the following expression.
$\dfrac{13\frac 79\div\frac23 \text{of} \frac13 + \frac23\times 3}{\frac 75 \text{of} 325 - 20 + 7}$
(A) $\frac{40}{1989}$
(B) $\frac{31}{2210}$
(C) $\frac{32}{221}$
(D) $\frac{33}{217}$

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Ans : (C) $\frac{32}{221}$

Q.5: The value of cosec $(58^o + \theta)-sec(32^o - \theta)$ + sin15^osin35^osec55^osin30^osec75^o is :
(A) 1
(B) 2
(C) $\frac12$
(D) 0

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Ans : (C) $\frac12$

Q.6: Some persons went on an outstation tour. The histogram shows their ages. How many persons are less than 20 years of age?

(A) 22
(B) 31
(C) 25
(D) 18

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Ans : (A) 22

Q.7: Study the given and answer the question that follows.

The total production of paper by company B in 2015 and 2017 to 2019 was what percentage less than 90% of the total production of paper by company A in 2014 to 2019 (correct to one decimal place)?
(A) 22.4%
(B) 19.6%
(C) 21.2%
(D) 17.5%

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Ans : (D) 17.5%

Q.8: In $\triangle ABC, D$ and E are points on AB and BC, respectively, such that DE is parallel to AC. If DE = 3 cm. AC = 5 cm and the area of trapezium ACED = 32 cm² , then what will be the area of $\triangle BDE$ ?
(A) $\frac {144}{17}$ cm²
(B) $\frac {48}{5}$ cm²
(C) 16 cm²
(D) 18 cm²

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Ans : (D) 18 cm²

Q.9: Study the given pie chart and answer the question that follows.
Total number of students admitted in a college = 700.
Distribution of the percentage of students in various caurses.

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Percentage-wise distribution of the number of boys.

Course	Number of boys
B. Sc. Maths	40%
B. Sc. Physics	68%
B. Sc. Chemistry	58%
B. Sc. Computer Science	80%
B. Com	75%
BBA	65%

(A) 3 : 7
(B) 4 : 7
(C) 3 : 5
(D) 2 : 5

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Ans : (C) 3 : 5

Q10: In a circle with centre O and radius 6.5 cm, a chord AB is at a distance 2.5 cm from the centre. If tangents at A and B intersect at P, then find the distance of P from the centre.
(A) 16.9 cm
(B) 18 cm
(C) 15 cm
(D) 17 cm

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Ans : (A) 16.9 cm

Q.11: What is the compound interest (in ₹) on a sum of ₹46,000 for $2\frac 25$ years at 15% per annum, interest being compounded annually ( nearest to a ₹) ?
(A) 18,458
(B) 18,485
(C) 19,485
(D) 19,458

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Ans : (B) 18,485

Q.12: If $\sqrt x + \frac {1}{\sqrt x} =2\sqrt{3}$ , then what will be the value of x⁴ + $\frac {1}{x^4}$ ?
(A) 10402
(B) 9606
(C) 9602
(D) 10406

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Ans : (C) 9602

Q.13: If 3x – 2y + 3 = 0 , then what will be the value of 27 x³ + 54xy + 30 – 8y³?
(A) -27
(B) 57
(C) -57
(D) 3

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Ans : (D) 3

Q.14: Chords AB and CD of a circle meet at point P (outside the circle), when produced, If AB = 9 cm, PB = $\frac 13$ AB and CD = 5 cm, then the length of PD (in cm ) is:
(A) 7
(B) 6
(C) 5
(D) 4

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Ans : (D) 4

Q.15: By selling an article for ₹3,150, a shopkeeper earns 5% profit. For how much money should he sell the article in order to gain 8% ?
(A) ₹3,240
(B) ₹3,180
(C) ₹3,200
(D) ₹3,250

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Ans : (A) ₹3,240

Q.16: Given that $3\sqrt{3x^3} - 8y^3 = (\sqrt3x + Ay) (3x^2 + By^2 + Cxy)$ , the value of (A² + B² – C²) is:
(A) 4
(B) 8
(C) 12
(D) 0

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Ans : (B) 8

Q.17: A solid metallic sphere of radius 12 cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed ?
(A) 24
(B) 96
(C) 864
(D) 216

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Ans : (D) 216

Q.18: A tap can fill a tank in 4 hours. Another tap can fill the same tank in 6 hours. If both the taps are opened at the same time, then in how much time will the empty tank be filled completely?
(A) 2 h 30 min
(B) 2 h 24 min
(C) 3 h
(D) 2 h

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Ans : (B) 2 h 24 min

Q.19: If $tan 3 \theta = sin45^o.cos45^o + cos60^o \text{and} 3\theta$ is an acute angle, then what will be the value of $sin4 \theta$ ?
(A) $\frac {\sqrt 3} {2}$
(B) $\frac {1} {\sqrt2}$
(C) $\frac 12$
(D) 1

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Ans : (A) $\frac {\sqrt 3} {2}$

Q.20: A boat can go 15 km downstream and 8 km upstream in 2 h. It can go 20 km downstream and 12 km upstream in 2 h 50 min. What is the speed (in km/h ) of the boat while going downstream?
(A) 16
(B) 15
(C) 20
(D) 18

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Ans : (B) 15

Q.21: Study the given pie chart and answer the question that follows.
The pie chart shows the distribution (degree wise) of the number of computers sold by a shopkeeper during five months.

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If the difference between the numbers of computers sold in May and the numbers of computers sold in February is x, then the value of x will be:
(A) 450
(B) 480
(C) 540
(D) 420

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Ans : (B) 480

Q.22: The average of 40 numbers is 48.2. The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5. The 38^th and 40^th numbers ?
(A) 48
(B) 49
(C) 47.5
(D) 48.5

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Ans : (C) 47.5

Q.23: If the five-digit number 457 ab is divisible by 3, 7 and 11, then what is the value of a² + b² – ab ?
(A) 49
(B) 36
(C) 24
(D) 33

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Ans : (A) 49

Q.24:
(A) 62.5%
(B) 37.98%
(C) 61.25%
(D) 51.6%

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Ans : (C) 61.25%

Q.25: If $tan \theta + cot \theta = 3$ , then what will be the value of $tan^2 \theta + cot^2 \theta$ ?
(A) 1
(B) 7
(C) 11
(D) -1

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Ans : (B) 7

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