SSC CGL MATHS
Tier-II (12 Sept 2019)
Instructions For the following questions answer them individually
Q.1 Two-third of the number of employees of a company are males and the rest are females. If ⅜ of the male employees and ⅖ female employees are temporary employees and the total number of permanent employees is 740. Then ⁷/₁₅ the total number of employees exceeds the number of temporary female employees by:
A 400
B 340
C 308
D 320
Answer: A
Q.2 Three fractions x,у and z are such that x > y > z.When small of them divided by the greatest, the result is ⁹/₁₆ , which exceeds y by 0.0625.If x+y+z=1¹³/₂₄,then the value of x+z is
A ⁷/₈
B 1
C ²⁵/₂₄
D ⁷/₆
Answer: C
Q.3 If the 11-digit number 5678x43267y is divisible by 72, then the value of √(5x+8y) is:
A 6
B 4
C 7
D 8
Answer: A
Q.4 What is the ratio of the third proportionalto 0.4 and 0.8, to the mean proportional between 13.5 and 0.24?
A 5 : 4
B 7: 8
C 8 : 9
D 9 : 10
Answer: C
Q.5 If x + ⅟₁₆x = 3 then the value of 16x3 + ⅟₂₅₆x3 is:
A 423
B 441
C 432
D 414
Answer: A
Q.6 If 60% of a number is 120 more than 20% of the number, then 28% of the number is less than 33⅓% of the number by:
A 14
B 12
C 16
D 15
Answer: C
Q.7 A sum lent out at simple interest amounts to ₹6076 in 1 year and ₹7504 in 4 years. The sum and the rate of interest p.a. are respectively:
A ₹5,600 and 9%
B ₹5,600 and 8.5%
C ₹5,400 and 9%
D ₹5,400 and 10%
Answer: B
Q.8 In △ABC , the medians AD, BE and CF meet at O. What is the ratio of the area of △ABD tothe area of △AOE ?
A 2 : 1
B 3 : 1
C 5 : 2
D 3 : 2
Answer: B
Q.9 If x + y + z = 2, xy + yz + zx = −11 and xyz = −12 , then what is the value of √(x3 + y3 + z 3 − 2) ?
A 6
B 12
C 9
D 8
Answer: A
Q.10 The value of ( 1⅓÷ 2⁶/₇ of 5⅗)÷( 6⅖÷ 4½ of 5⅓) × ( ¾× 2⅔÷ ⁵/₉ of 1⅕) = 1 + k ,where k lies between
A -0.07 and -0.06
B -0.08 and -0.07
C -0.06 and -0.05
D -0.05 and -0.04
Answer: A
Q.11 5 years ago, the ratio of the age of A to that of B was 4 : 5. Five years hence, the ratio of the age of A to that of B will be 6 : 7. If, at present, C is 10 years younger than B, then what will be the ratio of the present age of A to that of C?
A 3 : 2
B 5 : 4
C 4 : 3
D 5 : 3
Answer: B
Q.12 The area of the base of a right circular cone is 400π andits height is 15 cm. The curved surface area of the cone (in cm2 ) is:
A 480π
B 500π
C 450π
D 560π
Answer: B
Q.13 The given pie chart shows the quantity wise sales distribution of five products (A, B, C, D and E) of a company in 2016. Quantity wise sales distribution of five products (A, B, C, D and E)
If 1500 units of product D were sold in 2016 and the total number of units sold by the company in 2017 was 18% more than that sold in 2016, then the total units sold by the company in 2017 is:
A 6336
B 6390
C 6372
D 6354
Answer: C
Q.14 The given bar graph shows the imports and exports (in ₹ crores) of steel by a country from 2013 to 2017.
What is the ratio of the total imports in 2015 and 2017 to the total exports in 2013 and 2016?
A 11 : 4
B 9 : 8
C 25 : 21
D 9 : 11
Answer: C
Q.15 An article is sold at a certain price. If it is sold at 80% of this price, then there will be a loss of 10%. What is the percentage profit when the article is sold at the original selling price?
A 15½
B 12½
C 15
D 12
Answer: B
Q.16 In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is:
A 8.35 cm
B 9 cm
C 10.15 cm
D 9.25 cm
Answer: C
Q.17 The value of 
A ³/₂
B ½
C 1
D 2
Answer: D
Q.18 A is 25% more than B and B is 40% less than C. If C is 30% more than D, then by what percent is A less than D?
A 1.5
B 2.5
C 4
D 5
Answer: B
Q.19 In a class, 83⅓%of the number of studentsare girls and the rest are boys. If 60% of the number of boys and 80% of the number of girls are present, then what percentage of the total number of students in the class is absent?
A 26⅔
B 22⅔
C 23⅓
D 12⅓
Answer: C
Q.20 A spends 65% of his income. His income is increased by 20.1% and his expenditure is increased by 25%. His savings:
A Increase by 11%
B Increase by 5%
C Decrease by 5%
D Decrease by 11%
Answer: A
Q.21 The average weight of a certain numberofstudents in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weightof 80 kg join the group, the average weight of the students in the group decreases by 0.7 kg, The number of students initially in the group is:
A 56
B 46
C 44
D 54
Answer: B
Q.22 If (1+sinφ)/ (1-sinφ) =p2/q2, then secφ is equal to
A 2P2Q2/p2+q2
B ½(q/p+p/q)
C ⅟p2+⅟q2
D P2q2/p2-q2
Answer: B
Q.23 The marked price of an article is ₹800 and it is sold at a discount of 19%. If there is a gain of 8%, then by what percent above the cost price was the article marked?
A 33⅓
B 35
C 27
D 36⅔
Answer: A
Q.24 The base of a right prism is a triangle with sides 20cm, 21cm and 29cm. If its volume is 7560cm3, then its lateral surface area (in cm2 ) is:
A 2484
B 2556
C 2520
D 2448
Answer: C
Q.25 The expression √[10 + 2 ( √6 − √15 − √10)] is equal to:
A √3 + √2 − √5
B √3 − √2 − √5
C √3 − √2 + √5
D√2 − √3 −√5
Answer: A
Q.26 A cylindrical vessel of radius 3.5 m is full of water. If 15400 litres of water is taken out from it, then the drop in the water level in the vessel will be:
A 72 cm
B 40 cm
C 35 cm
D 60 cm
Answer: B
Q.27 The value of 
A 2cosφ
B cosecφ secφ
C 2sinφ
D sinφ cosφ
Answer: D
Q.28 A, B and C start a business. A invests 33⅓%of the total capital, B invests 25%of the remaining and C invests the rest. If the total profit at the end of a year is ₹1,62,000, then A’s share in profit is:
A ₹81,000
B ₹60,000
C ₹54,000
D ₹90,000
Answer: C
Q.29 A solid metallic sphere of radius 8 cm is melted and drawn into a wire of uniform cross-section. If the length of the wire is 24 m, then its radius (in mm) is:
A 6
B 5
C 5⅓
D 6 ⅔
Answer: C
Q.30 The sides of a triangle are 56 cm, 90 cm and 106 cm. The circumference of its circumcircle is:
A 106π
B 109π
C 108π
D 112π
Answer: A
Q.31 The speed of a boat in still water is 18 km/h and the speed of the current is 6 km/h. In how much time (in hours) will the boat travel a distance of 90 km upstream and the same distance downstream?
A 9½
B 11¼
C 12
D 10
Answer: B
Q.32 The HCF of two numbers is 21 and their LCM is 221 times the HCF. If one of the numbers lies between 200 and 300, then the sum of the digits of the other number is:
A 14
B 17
C 18
D 15
Answer: D
Q.33 △ABC and △DBC are on the same BC but on opposite sides of it. AD and BC intersect each other at O.If AO = a cm, DO = b cm and the area of △ABC = xcm2 , then what is the area(in cm2 ) of △DBC
A (a/b)x
B (ab/2)x
C bx /a
D (a+b)/2
Answer: C
Q.34 The value of tan2 φ + cot2 φ − sec2 φcosec2 φ is equal to
A -2
B 1
C 0
D -1
Answer: A
Q.35 The point of intersection of the graphs of the equations 3x – 5y = 19 and 3y -7x + 1 =0 is P ( α,β ). Whatis the value of ( 3α − β ) ?
A -2
B -1
C 1
D 0
Answer: B
Q.36 ( secφ − tanφ )2 ( 1 + sinφ )2 ÷ sin2 φ= ?
A cosφ
B cot2 φ
C secφ
D cos2 φ
Answer: B
Q.37 By selling two articles for ₹800, a person gains the cost price of three articles. The profit percent is:
A 125
B 140
C 120
D 150
Answer: D
Q.38 What is the compound interest on a sum of ₹7200 for 2⅖ years at 20% p.a., interest compounded yearly (nearest to an integer)?
A ₹4,290
B ₹3,960
C ₹4,205
D ₹3,997
Answer: D
Q.39 The value of 
A -1
B 1
C 3
D -3
Answer: A
Q.40 The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is 24√3 cm3. The volume (in cm3) of the pyramid is:
A 1152
B 480
C 576
D 384
Answer: D
Q.41 The sum of the interior angles of a regular polygonis 1260⁰, What is the difference between an exterior angle and an interior angle of the polygon?
A 105⁰
B 100⁰
C 120⁰
D 90⁰
Answer: B
Q.42 In circle with centre O. AC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and ∠AEB=68⁰ , then the measure of ∠DOC is
A 32⁰
B 30⁰
C 22⁰
D 44⁰
Answer: D
Q.43 In ΔABC, the perpendiculars drawn fromA,B and C meet the opposite sides at D,E and F, respectively.AD, BE and CF intersect at point P. If ∠EPD=116⁰ and the bisectors of ∠A and ∠B meet at Q, then the measure of ∠AQBis:
A 96⁰
B 122⁰
C 124⁰
D 64⁰
Answer: B
Q.44 The perimeters of two similar triangles ABC and PQR are 78 cm and 46.8 cm, respectively. If PQ = 11.7, then the length of AB is:
A 19.5 cm
B 23.4 cm
C 24 cm
D 20 cm
Answer: A
Q.45 If the diameter of the base of a right circular cylinder is reduced by 33⅓% and its height is doubled, then the volume of the cylinder will:
A increase by 1⅟₉%
B remain unchanged
C increase by 11⅟₉%
D decrease by 11⅟₉%
Answer: D
Q.46 A right circular solid cone of radius 3.2 cm and height 7.2 cm is melted and recast into a right circular cylinder of height 9.6 cm. What is the diameter of the base of the cylinder?
A 4.2 cm
B 4.5 cm
C 3.5 cm
D 3.2 cm
Answer: D
Q.47 40 litres of 60% concentration of acid solution is added to 35 litres of 80% concentration of acid solution. What is the concentration of acid in the new solution?
A 66%
B 66⅔%
C 69⅓%
D 69%
Answer: C
Q.48 In △PQR, I is the incentre of the triangle. If ∠QIR = 107∘, then what is the measure of ∠P?
A 37⁰
B 43⁰
C 73⁰
D 34⁰
Answer: D
Q.49 If x4− 83x2 + 1 = 0, then a value of x3 − x−3can be:
A 758
B 756
C 739
D 737
Answer: B
Q.50 Sujata marks an article 36% above the cost price and allows a 40% discount on the marked price. The loss percentage is:
A 15
B 16.8
C 18.4
D 4
Answer: C
Q.51 If 3(cot2 φ −cosφ) = cos2φ, 0⁰ < φ < 90⁰ 2, then the value of (tan2 φ + cosec2 φ +sin2 φ) is:
A ¹³/₃
B ⁶¹/₁₂
C ²⁵/₁₂
D ¹⁵/₄
Answer: B
Q.52 A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
A 72
B 54
C 36
D 27
Answer: C
Q.53 If (5x + 1)3 + (x − 3)3 + 8(3x − 4)3 = 6(5x + 1)(x − 3)(3x − 4) , then x is equal to:
A ⁵/₆
B ⅓
C ⅔
D ¾
Answer: A
Q.54 The average of 33 numbers is 74. The average of the first 17 numbers is 72.8 and that of the last 17 numbers is 77.2. If the 17th number is excluded, then what will be the average of the remaining numbers (correct to one decimal place)?
A 72.9
B 73.4
C 71.6
D 70.8
Answer: A
Q.55 A solid cube is cut into three cuboids of same volumes. Whatis the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
A 9 : 10
B 27 : 16
C 20 : 10
D 9 : 8
Answer: A
Q.56 (sin2 φ − 3sinφ + 2)/cos2 φ = 1 where 0⁰ < φ < 90⁰ , then what is the value of (cos2φ + sin3φ + cosec2φ) ?
A (2- √3)/ 3
B (3- 4√3)/ 6
C (9- 4√3)/ 6
D (3- 2√3)/ 3
Answer: C
Q.57 A loan has to be returned in two equal yearly instalments each of ₹44,100. If the rate of interest is 5% p.a.. compounded annually, then the total interest paid is:
A ₹5,840
B ₹6,000
C ₹6,200
D ₹6,280
Answer: C
Q.58 A sum of ₹x is divided among A, B and C such that the ratio of the shares of A and B is 6 : 7 and that of B and is 3 : 2. If the difference between the shares of A and C is ₹540, then the value of x is:
A 7425
B 7020
C 7155
D 7290
Answer: C
Q.59 The sides PQ and PR of △PQR are produced to points S and T , respectively. The bisectors of ∠SQR and ∠TRQ meet at U . If ∠QUR = 79∘ , then the measure of ∠P is:
A 41⁰
B 49⁰
C 22⁰
D 23⁰
Answer: C
Q.60 The value of 
A 2
B -1
C -2
D 0
Answer: B
Q.61 Alloy A contains copper and zine in the ratio of 4 : 3 and alloy B contains copper and zine in the ratio of 5: 2. A and B are taken in the ratio of 5 : 6 and melted to form a new alloy. The percentage of zinc in the new alloy is closest to:
A 54
B 34.2
C 36.8
D 35
Answer: D
Q.62 If the price of petrol increases by 19%, and Sunitha intends to spend only an additional 12% on petrol, by what percent should she reduce the quantity of petrol purchased (nearest to an integer)?
A 7
B 6
C 5
D 8
Answer: B
Q.63 The value of 
A cosecφ
B ½
C secφ
D 1
Answer: D
Q.64 A, B and C invested their capital in the ratio of 2 : 3 : 5. The ratio of months for which A, B and C invested is 4 : 2 : 3. If C gets a share of profit which is ₹1,47,000 more than that of A, then B’s share of profit is:
A ₹1,26,000
B ₹1,68,000
C ₹1,05,000
D ₹1,89,000
Answer: A
Q.65 In a quadrilateral ABCD, the bisectors of ∠A and ∠D meet at E. If ∠CED=560 and ∠A=490, then the measure of ∠B is:
A 710
B 540
C 630
D 670
Answer: C
Q.66 If 8x3 − 27y3 = (Ax + By)(Cx2 − Dy2 + 6xy),then (A + B + C − D) is equal to:
A -12
B 12
C 15
D 9
Answer: B
Q.67 The number of factors of 3600 is:
A 45
B 44
C 43
D 42
Answer: A
Q.68 The given pie chart shows the quantity wise sales distribution of five products (A, B, C, D and E) of a company in 2016. Quantity wise sales distribution of five products (A, B, C, D and E)
If 320 units of product A were sold by the company, then how many units of products B and E together were sold by the company?
A 567
B 576
C 512
D 640
Answer: B
Q.69 4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can do it in 10 days. To complete the same work in 7 days, how many women should assist 4 men?
A 11
B 14
C 12
D 13
Answer: D
Q.70 If x = (164)169 + (333)337 − (727)726 , then what is the units digit of x?
A 5
B 7
C 8
D 9
Answer: C
Q.71 Pipes A and B can fill a tank in 16 hours and 24 hours, respectively. and pipe C alone can empty the full tank in x hours. All the pipes were opened together at 10:30 a.m., but C was closed at 2:30 p.m. If the tank was full at 8:30 p.m. on the same day, then what is the value of x?
A 64
B 48
C 45
D 96
Answer: D
Q.72 Let x be the least number which when divided by 15, 18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?
A 39
B 37
C 43
D 36
Answer: A
Q.73 The given bar graph shows the imports and exports (in ₹ crores) of steel by a country from 2013 to 2017.
The total imports of steel in 2014, 2016 and 2017 is what percent less than the total exports in 2013, 2015 and 2017 (correct to one decimal place)?
A 13.4
B 15.8
C 16.2
D 14.5
Answer: D
Q.74 A person sells an article at 16% below its cost price. Had he sold it for ₹33 more, he would have gained 14%. To gain 25%, he should sell the article for:
A ₹128
B ₹137.5
C ₹135
D ₹130.5
Answer: B
Q.75 The given bar graph shows the imports and exports (in ₹ crores) of steel by a country from 2013 to 2017.
In how many years were the imports more than 80% of the average exports (per year) of the country during the given 5 years?
A 4
B 2
C 1
D 3
Answer: D
Q.76 Renu was sitting inside train A, which was travelling at 50 km/h. Another train, B, whose length was three times the length of A crossedher in the opposite direction in 15 seconds. If the speed of train B was 58 km/h, then the length of train A (in m) is:
A 210
B 180
C 160
D 150
Answer: D
Q.77 The given graph shows the marks obtained by students in an examination.
The number of students who obtained less than 300 marks is what percent more than the number of students who obtained 350 or more marks?
A 80%
B 28%
C 44.4%
D 22.7%
Answer: A
Q.78 In △ABC , AB = ACand is a point on BC. If BD = 5 cm, AB = 12 cm and AD = 8 cm, then the length of CD is:
A 14.8 cm
B 16.2 cm
C 16 cm
D 14 cm
Answer: C
Q.79 The ratio of the incomes of A and last year was 4 : 3, respectively. The ratios of their individual incomes of the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income for the present year is ₹8.04 lakh, then the income of B last year was:
A ₹2.7 lakh
B ₹3.6 lakh
C ₹2.4 lakh
D ₹2.8 lakh
Answer: A
Q.80 When a two-digit numberis multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum ofthe digits of the given number is:
A 6
B 9
C 8
D 7
Answer: C
Q.81 To do a certain work,the ratio of the efficiencies of X and Y is 5 : 4. Working together, they can complete the same work in 10 days. Y alone starts the work and leaves after 5 days. The remaining work will be completed by X alone in:
A 14 days
B 12 days
C 15 days
D 10 days
Answer: A
Q.82 The bisector of ∠B in △ABC meets AC at D. If AB =10cm, BC = 11cm and AC = 14cm, then the length of AD is:
A 6cm
B ²²/₃cm
C 7cm
D ²⁰/₃cm
Answer: D
Q.83 The value of 
Answer: A
Q.84 A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and ∠B = 90∘ . If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle?
A 20 π
B 18 π
C 15 π
D 12 π
Answer: B
Q.85 Places A and B are 396 km apart. Train X leaves from A for B and train Y leaves from B for A at the same time on the same day onparallel tracks. Both trains meet after 5½ hours. The speed of Y is 10 km/h more than that of X. What is the speed (in km/h) of Y?
A 41
B 54
C 31
D 56
Answer: A
Q.86 If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio of its diameter to its height?
A 5 : 2
B 1 : 1
C 2 : 1
D 4 : 1
Answer: D
Q.87 A sum amounts to ₹14,395.20 at 9.25 % p.a. simple interest in 5.4 years. What will be the simple interest on the same sum at 8.6 % p.a. in 4.5 years?
A ₹3,715.20
B ₹3,627
C ₹3,797.76
D ₹3,672
Answer: A
Q.88 When an article is sold at its marked price, it gives a profit of 25%. If a discount of 9.6% is allowed on the marked price, then the profit percent will be:
A 13
B 15.4
C 15
D 16.6
Answer: A
Q.89 A man sells his goods at a certain price, 20% of which is his profit. If the price at which he buys the goods increases by 10% and he sells them at an 8% higher price, then what will be his profit percent (correct to one decimal place)?
A 21.8
B 23.4
C 21.4
D 22.7
Answer: D
Q.90 The given pie chart shows the quantity wise sales distribution of five products (A, B, C, D and E) of a company in 2016. Quantity wise sales distribution of five products (A. B, C, D and E)
In 2016,if a total of 14616 units were sold, then the number of units of products D sold was:
A 4263
B 4872
C 4060
D 4096
Answer: C
Q.91 The value of 9 × 6 ÷ 24 + 8 ÷ 2 of 5 − 30 ÷ 4 of 4 + 27 × 5 ÷ 9 is:
A ⁶⁴⁷/₄₀
B ²⁴³/₈
C ⁴⁹³/₈
D ²⁵⁹/₈
Answer: A
Q.92 A field roller, in the shape of a cylinder, has a diameter of 1 m and length of 1¼m. If the speed at which the roller rolls is 14 revolutions per minute, then the maximum area (in m2 ) that it can roll in 1 hour is: (Take π = ²²/₇)
A 3960
B 3600
C 3300
D 3560
Answer: C
Q.93 If the volume of a sphere is 4851cm3 , then its surface area (in cm2) is: (Take π = ²²/₇)
A 1386
B 2772
C 1323
D 1337
Answer: A
Q.94 From a point exactly midway between the foot of two towers P and Q,the angles of elevation of their tops are 30∘ and 60∘ , respectively. The ratio of the height of P to that of Q is:
A 1 : 3
B 1 : 2
C 1 : 2√3
D 2 : 3√3
Answer: A
Q.95 The graphs of the equations 2x + 3y = 11 and x − 2y + 12 = 0 intersects at P(x1,y1 ) and the graph of the equations x − 2y + 12 = 0 intersects the x-axis at Q(x2,y2 ) . What is the value of (x1 − x2 + y1 + y2 ) ?
A 13
B -11
C 15
D -9
Answer: C
Q.96 If x = (√5-√3)/(√5+√3) and y is the reciprocal of x , then what is the value of (x3 + y3 )?
A 488
B 504
C 472
D 476
Answer: A
Q.97 A man starts from his house and travelling at 30 km/h, he reacheshis office late by 10 minutes, and travelling at 24 km/h, he reachesh is office late by 18 minutes. The distance (in km) from his house to his office is:
A 18
B 16
C 12
D 20
Answer: B
Q.98 The value of (tan29∘ cot61∘ − cosec2 61∘ ) + cot2 54∘ − sec2 36∘ + (sin2 1∘ + sin2 3∘ + sin2 5∘ + − − − + sin2 89∘ ) is:
A 20½
B 21
C 22½
D 22
Answer: A
Q.99 If √(10 − 2√21) + √(8 + 2√15) = √a + √b , where a and b are positive integers, then the value of √(ab) is closest to:
A 4.6
B 5.9
C 6.8
D 7.2
Answer: B
Q.100 A can do 40% of a work in 12 days, whereas B can do 60% of the same work in 15 days. Both work together for 10 days. C completes the remaining work alone in 4 days. A, B and C together will complete 28% of the same work in:
A 2½days
B 3days
C 1½days
D 2 days
Answer: D
