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SSC CGL MAINS/ QUANTITATIVE APTITUDEQ.1. Ram got twice as many marks in English as in

Science. His total marks in English, Science and Maths are 180. If the ratio of his marks in English and Maths is 2 : 3, what are his marks in science?

(A) 30 (B) 60 (C) 72 (D) 90Q.2. The average of 1, 3, 5, 7, 9, 11, ... to 25 terms is (A) 125 (B) 25 (C) 625 (D) 50Q.3. In a town out of adult population 45% men and

25% women are adult population. If it is known that a man cannot marry to more than one woman and a no of the woman can marry to more than one man, then what % is the population of married to total population?

(A) 24.18% (B) 30.16% (C) 32.14% (D) 28.12%Q.4. If

( )( ) ( )( ) ( )( )2 2 2

x y z

b c b c a c a c a b a b a b c= =

− + − − + − − + − , then the value of (x+y+z) is

(A) 0 (B) a + b + c (C) a2 + b2 + c2 (D) 3

Q.5. Three persons A, B and C whose salaries together amount to Rs.36000 they spend 80%, 85% and 75% of their salaries respectively. If their savings are in the ratio 8 : 9 : 20, then C's salary is

(A) 10000 (B) 16000 (C) 12000 (D) 8000

Q.6. Cost of two articles were in the ratio of 16 : 23. The cost of first article increased by 10% and that of second by Rs.477. Now the costs of two articles are in the ratio of 11 : 20. The price of the second article (in Rs.) in the beginning was -

(A) 932 (B) 1219 (C) 1619 (D) 848

Q.7. The speed of a train relative to a moving car is 70 km/h more. The car accelerates and start moving at a speed 10% more than before. Both now travel for 3 hours and the train covers a total distance of 750 km. How much distance did the car travel?

(A) 644 km (B) 354 km (C) 594 km (D) 185 km

Q.8. If the compound interest on a certain sum for two years at 12.5% p.a. is 4080, the simple interest on the same sum at the same rate of interest for the same period of time is -

(A) 3200 (B) 3600 (C) 3680 (D) 3840

Q.9. Two stations A and B are 465 km a part . One train start from A to B at 10:00a.m. at the speed of 65 km/hr another train start from B to A at 11a.m. at the speed of 35km/hr then what time they meet each other at ?

(A) 2 pm (B) 3 pm (C) 4: 30 pm (D) 1 pm

Q.10. P and Q can do a piece of work in 8 days, Q and R can do it in 24 days, while R and P can do it in 4

87

days. In how many days can P do it alone? (A) 60 (B) 40 (C) 30 (D) 10Q.11. In a two – digit number, the digit at the unit’s place

is 1 less than twice the digit at the ten’s place. If the places of both digits are interchanged, the new number formed is 27 more than the original number. The original number is -

(A) 47 (B) 59 (C) 23 (D) 35Q.12. A train 300 m. long is running with a speed of 54

kmph. In what time will it cross a telephone pole? (A) 20 (B) 15 (C) 17 (D) 18

Q.13. If a+b+c = 0, then what is the value of 2 2 2a b c

bc ac ba+ + ?

(A) - 3 (B) 0 (C) 1 (D) 3Q.14. Find the value of x, if (14x - 4) : (8x -1) = (3x + 8) : (9x + 5)

(1) 1 (B) 3 (C) 2 (D) 4Q.15. If (a + b) : (b + c) : (c + a) = 5 : 6 : 9 and a + b + c

= 10. What is the value of C. (A) 3 (B) 4 (C) 5 (D) 6Q.16. A mixture contains milk and water in the ratio 5:1.

On adding 4 litres of water, the ratio of milk and water becomes 5:2. What is the quantity of milk in the original mixture?

(A) 5 (B) 25 (C) 20 (D) 22.5Q.17. The ratio of number of girls to the number of boys

is 1 : 2. If the average weight of the boys is 30kg and the average weight of both the boys and girls is 25 kg. Then the average weight of the girls is -

(A) 24 (B) 21 (C) 18 (D) 15Q.18. A reduction of 20% in the price of sugar enables

a housewife to purchase 6 kg. more for Rs. 240. What is the original price per kg. of sugar?

(A) 10 (B) 8 (C) 6 (D) 5

Multan Sultans' 30-year-old South African batsman Rilee Rossouw smashed the fastest ever hundred in the history of Pakistan Super League.

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Q.19. If 2 3x = + then 22

1x

x+ equals to

(A) 12 (B) 13 (C) 14 (D) 15Q.20. If a + b + c = 45 and ab + bc + ca = 254. Find the

value of a2 + b2 + c2 = ? (A) 1517 (B) 1516 (C) 1515 (D) 1518Q.21. Rs. 8000 invested at compound interest gives Rs.

1261 as interest after 3 years. The rate of interest per annum?

(A) 25 (B) 17.5 (C) 10 (D) 5Q.22. Find the remainder when 103 + 113 + 123 + 133

+ 143 + 153 is divided by 75. (A) 6 (B) 5 (C) 2 (D) 0Q.23. In one litre of a mixture of alcohol and water,

water is 30%. The amount of alcohol that must be add to the mixture so that the part of water in the mixture becomes 15% is -

(A) 1000 (B) 700 (C) 300 (D) 900Q.24. If the area of a rectangle be (x2+7x+10) m2, then

one of the possible perimeter of it is? (A) (2x + 7) (B) (4x + 10) (C) (x + 14) (D) (4x + 14)Q.25. 20 men could complete a work in 80 days. They

worked together for 60 days, after that due to bad whether the work is stopped for 10 days. How many more men should be employed so as to complete the work in time?

(A) 10 (B) 5 (C) 20 (D) 30Q.26. A money lender finds that due to fall in the annual

rate of interest from 8% to 7 (3/4)% of his yearly income diminishes by Rs.61.50. His capital is?

(A) 22400 (B) 23800 (C) 24600 (D) 26000Q.27. A person has to cover 6km in 45 minute. If he

covers half of the distance in (2/3) time then what will be the speed of man for covering the remaining distance in remaining time?

(A) 3 (B) 8 (C) 12 (D) 15Q.28. If x2-3x+2 is factor of f(x)=x5-5x4+Ax3+Bx2+4

x-40, then A, B is? (A) – 20, 60 (B) 30, 50 (C) 40, 40 (D) 10, 70Q.29. A merchant fixes the sale price of his goods at 25%

above the cost price. He sells his goods at 15% less than the fixed price. What will be his percentage profit or loss?

(A) 6.25% profit (B) 7.25% profit (C) 6.25% loss (D) 7.25% lossQ.30. A, B and C earns total Rs.1450 and spends 60%,

65% and 70% of own’s income respectively. If his savings in the ratio of 14:21:15. Then find the salary of B?

(A) 450 (B) 500 (C) 600 (D) 750Q.31. The ratio of expenditure and savings is 3:2. If the

income increases by 15% and the saving increases by 6%, then by how much percent should his expenditure increases?

(A) 12 (B) 21 (C) 24 (D) 25Q.32. The present ratio of ages of A and B is 4: 5. 18

years ago, this ratio was 11:16. Find the total age of their present age?

(A) 90 (B) 80 (C) 105 (D) 110Q.33. Dev and Ram can do a piece of work in 45 days

and 40 days respectively. They began the work together, but Dev leaves after some days and Ram finished the remaining work in 23 days. After how many days did Dev leave?

(A) 4 (B) 5 (C) 8 (D) 9Q.34. The ratio of A’s income and B’s income last year

was 3:4. The ratio of their own income of last year and this year is 4:5 and 2:3 respectively. If the total sum of their present income is Rs.4160, then find the present income of A?

(A) 1500 (B) 1600 (C) 1760 (D) 2560Q.35. The schedule working hour of a labour in a

week is 48 hours and he gets rs. 480 for that. Over time rate is 25% more than the basic salary rate. In a week a labour gets Rs 605, how many hours altogether he works in that week?

(A) 59 (B) 55 (C) 58 (D) 52Q.36. A businessman sells a commodity at 10% profit.

If he had bought it at 10% less and sold it for Rs.2 less, the he would have gained 16(2/3) %. The cost price of the commodity is?

(A) 40 (B) 56 (C) 75 (D) 85Q.37. In an examination in which full marks were 500.A

got 25% more than B, B got 20% less than C. If A got 360 marks. What percentage of full marks was obtained by C?

(A) 50 (B) 60 (C) 72 (D) 80Q.38. The speed of rickshaw, car and scooter are in

the ratio of 3 : 4 : 5. What is the ratio of the time

The central government permitted airlines operating in India to provide in-flight Wi-Fi services to passengers.

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taken by each one of them for covering the same distance?

(A) 2: 3: 4 (B) 1: 2: 3 (C) 20: 15: 12 (D) 5: 4: 3

Q.39. If 2 22 2

1 14a b

a b+ + + = then find the value of a2 + b2

(A) 1 (B) 2 (C) 1.5 (D) 2.5Q.40. A milkman buys milk at the rate of 6.40 Rs./ litre.

He added some water in it, then he sold the mixture at the rate of 8 Rs./litre and earned 37.5% profit. Find the ratio of milk and water for consumer.

(A) 10: 1 (B) 10: 3 (C) 5: 4 (D) 12: 5

Q.41. If a + b + c = 3, a2 + b2 + c2 = 6 and 1 1 1

1a b c

+ + =where a, b and c are all non - zero numbers, then abc is equal to

(A) 0 (B) 1 (C) 2/3 (D) 3/2

Q.42. If 2 2 613a b+ = then what will be the value of (a + b)/(a + b)?

(A) 631 (B) 99 (C) 647 (D) 651Q.43. Some articles had bought in Rs.840. If (1/3)

articles sold at 20% loss, then for getting overall 10% profit, then remaining articles would be sold at how much % profit?

(A) 25% (B) 12% (C) 28% (D) 30%Q.44. A tap can fill a cistern in 40 minutes and a second

tap can empty the filled cistern in 60 minutes. By mistake without closing the second tap, the first tap was opened. In how many minutes will the empty tank be filled?

(A) 72 (B) 84 (C) 108 (D) 120Q.45. If 1 is added to both the numerator and the

denominator of a fraction, it becomes 1/ 4 If 2 is added to both the numerator and the denominator of that fraction, it becomes 1/3 The sum of numerator and denominator of the fraction is-

(A) 8 (B) 13 (C) 22 (D) 27Q.46. The length of a train and that of a platform are

equal. If with a speed of 90 km/hr. the train crosses the platform in one minute, the length of the train is-

(A) 650 (B) 750 (C) 640 (D) 780Q.47-50. Study the following pie chart carefully

and answer the questions asked based on it. The following bar chart shows the production

(in thousands) of motorcycles by two companies A and B from 2010 to 2014 and the Pie – chart shows the percentage sale of these companies in respective years.

Q.47. What is ratio of the total number of motorcycles sold by Company B in 2011 to that sold by Company A in 2013?

(A) 27 : 23 (B) 31 : 29 (C) 37 : 33 (D) 39 : 34Q.48. The total no. of motorcycles sold by Company

A in 2014 is approximately what per cent of that produced by Company B in that year?

(A) 36% (B) 45% (C) 54% (D) 62%Q.49. What is the average number of motorcycle sold by

Company B in the given five years? (A) 39645 (B) 41315 (C) 42408 (D) 44606Q.50. What is the approximate percentage rise/fall in the

sale of Company A from 2011 to 2012? (A) 87% (B) 25% (C) 60% (D) 65%

Fitch Solutions cut its forecast for India's economic growth to 4.9 per cent in the current fiscal that ends March 31.

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Q.51. If (x + 2) is a common factor of x2 + ax +b and x2 + bx + a, then the ratio a : b is equal to.

(A) 3: 4 (B) 2: 1 (C) 1: 1 (D) 4: 3

Q.52. If a2 – 3a + 1 = 0, then the value of a5 + 5

1

ais equal

to (A) 123 (B) 125 (C) 135 (D) 201Q.53. The radii of two concentric circles are 13 cm and 8

cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and the bigger circle at E. Point A is joined to D. The length of AD is -

(A) 20 cm. (B) 19 cm. (C) 18 cm. (D) 17 cm.Q.54. If tan θ + tan ψ = x and cot θ + cot ψ = y, then what

is the value of cot (θ + ψ)?

(A) 1 1

x y+ (B)

1 1

x y− (C) y (D) x – y

Q.55. The expression o o

o o

tan 57 cot 37

tan 33 cot 53

++

is equal to

(A) tan 33o cot 53o (B) tan 53o cot 37o

(C) tan 33o cot 57o (D) tan 57o cot 37o

Q.56. If ( ) ( )2 2

x cos 3 x sin 1 0θ − + θ − = then the

value of x tan sec

x sec tan

θ + θθ + θ is equal to

(A) 4

5 (B)

5

4 (C)

3

4 (D) 5

4

Q.57. The parallel sides of a trapezium are in a ratio 2 : 3 and their shortest distance is 12 cm. If the area of the trapezium is 480 sq. cm, the longer of the parallel sides is of length:

(A) 16 cm. (B) 32 cm. (C) 12 cm. (D) 48 cm. Q.58. If p4 + p2q2 + q4 = 6 and p2 + pq + q2 = 2 the find the

value of pq. (A) 1 (B) 0 (C) – 1/2 (D) 1/2Q.59. The equation of two parallel lines are 4x + 3y = 11

and 8x + 6y = 15 respectively. Find the distance between these lines.

(A) 7 (B) 9 (C) 9

10 (D)

7

10

Q.60. If 12x 5

3x+ = , find the value of 2

5x

6x 30x 1+ +.

(A) 1

5 (B)

1

7 (C)

1

9 (D)

1

6

Q.61. If x = 3 3 8 7 4 3+ + − then find the value of x. (A) 1 (B) 2 (C) 0 (D) – 2

Q.62. If sin cos

4sin cos

θ + θ =θ − θ then the value of 4 4sin cosθ − θ

is

(A) 8

17 (B)

9

17 (C) 7

17 (D) 16

32

Q.63. There are two equal circles of radius 3 cm each and the distance between their centres is 10 cm. The length of one of their transverse common tangent is-

(A) 10 cm. (B) 9 cm. (C) 8 cm. (D) 7 cm.Q.64. If 7 times the seventh term of an Arithmetic

Progression (AP) is equal to 11 times its eleventh term, then the 18th term of the AP will be

(A) 1 (B) 0 (C) 2 (D) – 1Q.65. Area of 4 walls of a cuboid is 448 sq. cm, its length

is 18 cm and height is 8 cm. What is its breadth (in cm)?

(A) 10 (B) 9 (C) 8 (D) 7Q.66. If p + q + r = 19, p2 + q2 + r2 = 133 and pr = q2, then

the difference between r and p is: (A) 5 (B) 3 (C) 6 (D) 4Q.67. If 4 – 2 sin2 θ – 5 cos θ = 0, 0o < θ < 90o, then the

value of sin θ + tan θ is:

(A) 3 2 (B) 3 3

2 (C)

3 2

2 (D) 2 3

Q.68. If 5x 3

73 2 3 1

2 2 4

− + =, then what is the value of x?

(A) 35/24 (B) 24/35 (C) – 24/35 (D) – 35/24Q.69. A circle is inscribed in a triangle ABC. It touches

the sides AB, BC and AC at the points R, P and Q respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of the triangle ABC is:

(A) 28 cm. (B) 30.5 cm. (C) 32 cm. (D) 26.5 cm.Q.70. What is the sum of the first 12 terms of an

arithmetic progression if the 3rd term is – 13 and the 6th term is – 4?

(A) 67 (B) 45 (C) – 30 (D) – 48Q.71. What is the reflection of the point (5, 2) in the line

x = – 3? (A) (– 11, 2) (B) (– 11, – 2) (C) (11, – 2) (D) (11, 2)

Nokia's Board of Directors has appointed Pekka Lundmark as President and Chief Executive Officer of Nokia.

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Q.72. Slope of the line AB is 4

3− . Co-ordinates of points

A and B are (x, – 5) and (– 5, 3) respectively. What is the value of x?

(A) – 1 (B) 2 (C) – 2 (D) 1Q.73. Find the unit digit of 771 + 663 × 365. (A) 1 (B) 2 (C) 3 (D) 4

Q.74. sec tan 1

tan sec 1

θ + θ −θ − θ + is equal to

(A) 1 sin

cos

− θθ

(B) 1 sin

1 cos

+ θ− θ (C)

cos

1 sin

θ− θ (D)

cos

1 sin

θ+ θ

Q.75. If 1 1 1

n n= +

+l l, then the value of l3 – n3 is:

(A) 3 (B) 2 (C) 1 (D) 0Q.76. In a triangle DEF, points A, B and C are taken on

DE, DF and EF respectively such that EC = AC and CF = BC. If ∠ D = 40o then what is the value of ∠ ACB?

(A) 140o (B) 70o (C) 100o (D) 135o

Q.77. The perimeter of the triangular base of a right prism is 15 cm and radius of the in -circle of the triangular base is 3 cm. If the volume of the prism be 315 cm3, then the height of the prism is-

(A) 60 cm. (B) 15 cm. (C) 12 cm. (D) 14 cm.Q.78. The internal radius of a hollow sphere is 5 2 cm.

The volume of a cube which will fit inside the sphere is -

(A) 1000 cm.3 (B) 100 2 cm.3

(C) 500 cm.3 (D) 1000 π cm.3

Q.79. The median drawn to one of the equal side of an isosceles triangle divides its perimeter into two parts 15 cm and 6 cm in length. Find the length of the base of the triangle.

(A) 5 cm. (B) 3 cm. (C) 1 cm. (D) 1.5 cm.Q.80. PQRS is a cyclic quadrilateral. QP and RS

produced meet at T. PS and QR produced meet at U. ÐT = 24o, ÐU = 36o. Find the value of ÐPQR.

(A) 60o (B) 48o (C) 120o (D) 85o

Q.81. If ( )21a 1 3

a+ = , then the value of 3

3

1a

a+ is

(A) 9 (B) 18 (C) 27 (D) 1

Q.82. If a + b + c = 5, a2 + b2 + c2 = 8 and 1 1 12

a b c+ + =

where a, b and c are all non -zero, then abc is-

(A) 1 (B) 2

17 (C)

17

2 (D)

17

4Q.83. A metallic cuboid 8 × 6 × 4 cm.3 is melted. The

minimum volume of molten metal which should be added to mould it into a cube whose edge is 'x' where 'x' is an integer, is

(A) 20 cm.3 (B) 24 cm.3

(C) 23 cm.3 (D) 21 cm.3

Q.84. If x sin 60o tan 30o – tan2 45o = cosec 60o cot 30o – sec2 45o, then what will be the value of x?

(A) 2 (B) – 2 (C) 6 (D) – 4

Q.85. If cosa

cos

θ =φ

, sinb

sin

θ =φ

, then sin2φ is equal to -

(A) 2

2 2

a 1

a b

−+ (B)

2

2 2

a 1

a b

+−

(C) 2

2 2

a 1

a b

−−

(D) 2

2 2

a 1

a b

++

Q.86. If PT is a tangent and AB is a chord of circle and they intersect at the point P externally and 2PT = AP and AB = 18 units, then PT is equal to

(A) 6 units (B) 9 units (C) 12 units (D) 15 units

Q.87. A rectangular field is 20 m long and 14 m wide. There is a path of equal width all around it, having an area 111 sq. m. Find the width of the path.

(A) 1.5 m. (B) 2.0 m. (C) 2.5 m. (D) 3.0 m.

Q.88. A wheel of radius 1.4 m. of a vehicle makes 40 revolutions in 1 min. What is the speed of the vehicle?

(A) 22.7 km/h (B) 22.4 km/h

(C) 21.12 km/h (D) 19.6 km/h

Q.89. If three circles with centers A, B, C respectively touches each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, then the radius of the circle with center A is-

(A) 2 cm. (B) 4 cm. (C) 3 cm. (D) 1 cm.

Q.90. If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder, Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the difference of the numbers.

(A) 5 (B) 7 (C) 9 (D) 11

Uttar Pradesh Chief Minister Yogi Adityanath inaugurated the new office of the police commissioner in Sector 108, Noida.

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Q.91. A cone of height 9 cm. with diameter of its base 18 cm. is carved out from a wooden soiled sphere of radius 9 cm. The percentage of the wood wasted is -

(A) 50% (B) 25% (C) 40% (D) 75%Q.92. If the area of circular ring having inner and outer

radius 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R1 and height h, then h in terms of R1 will be:

(A) 1

1

40 R

R

− (B) 12

1

40 R

R

−

(C) 2

1

1

40 R

R

− (D)

21

21

40 R

R

−

Q.93. A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

(A) 10 m (B) 15 m (C) 20 m (D) 17 m

Q.94. A map is drawn using the scale 1 cm : 400 kms. If the distance shown on the map between Delhi and Patna is 1

22

cms, what is the actual distance between the two cities?

(A) 800 km. (B) 1000 km. (C) 1250 km. (D) 1600 km.Q.95. The angle of elevation of a cloud from a point 60

m. above a lake is 30o and the angle of depression of the reflection of cloud in the lake is 60o. Find the height of the cloud?

(A) 100 m. (B) 120 m.

(C) 115 m. (D) 100 3 m.Q.96. A balloon is flying at some vertical constant height

from the ground with a speed of 10m/s, a man standing on the ground observes angle of elevation

to be 450. After 10 seconds he observes angle of elevation changed to 300. What is the height from the ground at which balloon is flying?

(A) ( )100 3 1+ m. (B) ( )150 3 1+ m.

(C) ( )50 3 1+ m. (D) ( )100 3 1− m.

Q.97-100. Study the following table and give the answer of the given questions.

Total number of players in different sports of a country and percentage of females.

Sports Total number of players

Percentage of females

Football 840 45Hockey 220 35Cricket 900 23Badminton 360 65Swimming 450 44Wrestling 540 40

Q.97. What is the total number of males in Football and Wrestling?

(A) 786 (B) 678 (C) 768 (D) 876Q.98. The total number of players in Badminton is

approximately what percent of the total number of players in Hockey.

(A) 149 (B) 178 (C) 157 (D) 164Q.99. What is the respective ratio of the number of

females in Badminton and Hockey together to the number of males in the same games?

(A) 311 : 269 (B) 268 : 319 (C) 269 : 311 (D) 319 : 268Q.100. What is the difference between the number of

males and number of females from all games? (A) 609 (B) 690 (C) 590 (D) 509

The historic City Chowk, the commercial hub in old Jammu, was renamed as 'Bharat Mata Chowk'.

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EXPLANATION/SSC CGL MAINS/ QUANTITATIVE APTITUDEQ.1.(A) English: Science = 2 : 1 English: Maths = 2 : 3

so marks in science = 1180 30

6× =

Q.2.(B) Sum of the terms =

[ ]252 1 24 2 625

2× + × =

Required average = 625/25 = 25Q.3.(C) 45 = 25% 100% = 180 Total population = 100 + 180 = 280 Married = (42 + 45) × 100/280 = 32.14%

Q.4.(A) ( )( ) ( )( ) ( )( )2 2 2

x y z

b c b c a c a c a b a b a b c= =

− + − − + − − + − = k x = k(b – c)(b + c – 2a), y = k(c– a)(c + a – 2b),

z = k(a– b)(a + b – 2c) x + y + z = k × {(b2 – c2 + c2 – a2 + a2 – b2) – 2[a(b

– c) + b(c – a) + c(a – b)])} x + y + z = 0Q.5.(B) Expenses are respectively = 80%, 85% and 75% Savings are respectively = 20%, 15% and 25% But given ratio between savings = 8 : 9 : 20 Ratio between income = 2 : 3 : 4 C's income = 16000Q.6.(B) Let the cost of both articles are 16x and 23x

respectively According to the question

16x × 110

100: 23x + 477 = 11 : 20

320x ×110

100 = 253x + 5247

352x - 253x = 5247 99x = 5247 x = 53 Cost of second article = 23 × 53 = 1219Q.7.(C) Speed of train = 750/3 = 250 km/h So the initial speed of car = 250 – 70 = 180 km/h Now the final speed of Car = 180 + 18 = 198 km/h Distance travelled by Car in 3 hours = 198 × 3 =

594 km

Q.8.(D) Let the sum be Rs.64 Compound interest for first year = 8 Compound interest for second year = 8 + 1 = 9 According to the question 9 + 8 = 4080 17 = 4080 1 = 240 64 = 240 × 64 = 15360 Simple interest for the same period at the same

rate of interest = 15360 × 25 × 2/ 200 = 3840Q.9.(B) D = 465 km 65 × 1 = 65 465 – 65 = 400km 65 × t + 35 × t = 400 t = 4 11 am + 4 = 3 pmQ.10.(D) P + Q = 8 15 units of work per day Q + R = 24 120 5 units of work per day R + P = 60/7 14 units of work per day According to the question P + Q + R = 17 units of work per day P = 12 units of work per day Required number of days = 120/12 = 10 days Q.11.(A) Go through options only 47 satisfy the given

conditions.

Q.12.(A) 3005

5418

× = 20

Q.13.(D)

( )( )

2 2 2 3 3 3

2 2 2 3

33

a b c a b c

bc ac ba abc

a b c a b c ab bc ca abc

abcabc

abc

+ ++ + =

+ + + + − − − +=

= =

Q.14.(A) Q.15.(C) a + b =5k ...(I) b + c = 6k ...(II) c + a = 9k ...(III) Adding all the three equations, we get

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2(a + b + c) = 20k 20 = 20k k = 1 Now, 2(a + b + c) = 20 × 1 (a + b + c) = 10 5 + c = 10 c = 5Q.16.(C) 5x/ (x+4) = 5/2 5x = 20 x = 4 5 × 4 = 20Q.17.(D) 30 x 25 2 1

25 x 5

2 1

−=

25 - x = 10 15 = x x = 15

Q.18.(A) 20 24010 .

80 6Rs× =

Q.19.(C)

2

2

2 3

12 3

14

116 2 14

x

x

xx

xx

= +

= −

+ =

+ = − =

Q.20.(A) a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca) = (45)2 – 2 × 254 = 2025 – 508 = 1517Q.21.(D)

3

3

1100

8000 1 9261100

92611

100 8000

211

100 201

100 205%

nr

A p

r

r

r

r

r

= +

+ =

+ =

+ =

=

=

3

3

1100

8000 1 9261100

92611

100 8000

211

100 201

100 205%

nr

A p

r

r

r

r

r

= +

+ =

+ =

+ =

=

=

Q.22.(D) n n n n na b c d e

a b c d e

+ + + ++ + + +

, remainder = 0 when n

= odd Since 10 + 11 + 12 + 13 + 14 + 15 = 75

Hence, 3 3 3 3 3 310 11 12 13 14 15

010 11 12 13 14 15

+ + + + + =+ + + + +

Q.23.(A) Amount of water in mixture = 1000 30300

100

× = (1000 + x) × 15/100 = 300 1000 + x = 2000 x = 1000 mlQ.24.(D) L × B = x2 + 7x + 10 = (x + 5) (x + 2) L = (x + 5) B = (x + 2) p = 2(L + B) p = 2(x + 5 + x + 2) p = 4x + 14Q.25.(C)

( )

20 60 3

20 80 420 101

4 20 80400 200 10

10 200

20

p

p

p

p

× =×

+ ×=

×= +=

=

Q.26.(C) 8-7 (3/4) % = 61.50 0.25% = 61.50 100% = 24600Q.27.(C) Remaining distance =3km Remaining time = (1/3) × 45 = 15 minute = (1/4)

hour Speed = [3/(1/4)] = 12kmph Q.28.(A) x2 - 3x + 2 = (x - 1) (x - 2) On putting x = 1 1 - 5 + A + B + 4 - 40 = 0 ....(I)

The head of the Bangladesh Bouddha Kristi Prachar Sangha Sanghanayaka Suddhananda Mahathero passed away in Dhaka. He was 88.

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offering (IPO).

On putting x = 2 32-80+8A+4B+8-40=0 ....(II) On solving both the equations, we get A=-20 and B=+60Q.29.(A)

25 1525 15 6.25%

100

× − − =

Q.30.(C) 40%=14 | 35%=21 | 30%=15 100%=35 | 100%=60 |100%=50 Ratio of income =35:60:50=7:12:10 Since, 7+12+10=29 unit=1450 Rs. 1 unit=50 Rs. Salary of B =12unit=12×50=600 Rs.Q.31.(B) Saving +expenditure = income 2+3=5 2×6+3×k=5×15 3k=63 K=21%Q.32.(A) Present age = A: B 18 year ago = A: B 4:5 ---------------------- 11:16 20:25----------------------11:16 9------18 years 1-----2 years Hence total age = (20+25)×2=90 yearsQ.33.(D)

23 40 451 9

40 40 45

× − = +

Q.34.(B) Ratio of last year of A: B=3: 4 Ratio of last year and present year of A = 4: 5 =

4 × (3/4): 5 × (3/4) = 3: (15/4) Ratio of last year and present year of B=2: 3 = 4:

6 (15/4) : 6=15: 24=5: 8 5x + 8x = 4160 x = 320 A = 5x = 5320 = 1600Q.35.(C) 605=48×10+12.5×k k=10 total work = 48+10 = 58Q.36.(A)

50 10 5010 5%

3 10010% 5% 5%

5% 2

100% 40

×− + − =

− ==

=

Q.37.(C)

100 100 100

360 72%125 80 500

× × × =

Q.38.(C) t1 : t2 : t3 = 1 2 3

1 1 1: :

v v v

= 1 1 1

: :3 4 5

= 20 : 15 : 12Q.39.(B)

2 22 2

2 2

2

2

2

2

2 2

1 12 2 0

1 10

10

1

1

10

1

1

1 1 2

a ba b

a ba b

aa

a

a

bb

b

b

a b

+ − + + − =

+ + − =

+ = =

=

− = =

=+ = + =

Q.40.(A) SP = 8

CP = 100 64

8137.5 11

× =

6.40 × x = 64

11× (x + y)

64 × x = 64

11× (x + y)

11x = 10x + 10y x = 10y x : y = 10 : 1Q.41.(D)

( ) ( )( )

( )

2 2 2 2 2

9 6 2

3

21 1 1

1

3

2

a b c a b c ab bc ca

ab bc ca

ab bc ca

a b c

ab bc ca abc

+ + = + + + + +

= + + +

+ + =

+ + =

+ + = =

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MAY 2020 MICAYoung Indian shuttlers Tasnim Mir and Mansi Singh won a bronze medal each in the girls'

singles event at the Dutch Junior International 2020 in Haarlem, Netherlands.

( ) ( )( )

( )

2 2 2 2 2

9 6 2

3

21 1 1

1

3

2

a b c a b c ab bc ca

ab bc ca

ab bc ca

a b c

ab bc ca abc

+ + = + + + + +

= + + +

+ + =

+ + =

+ + = =

Q.42.(C)

( )( )

2 2

2 2 2

2 2

2 2

2 2 2

2 2 2 2

613

613

613 612 613 612 613 612

613 612 1 1225

613 612 35

612 35

612

35

612 35 647

a b

a b

a b

a

b

a b

+ =+ =

− = − +

− = ×− =

+ = +==+ = + =

Q.43.(A)

( ) ( ) ( )1 220 1 10

3 320 2 30

2 50

25

k

k

k

k

× − + × =

− + ==

=

Q.44.(D) Work in 1 minute = 1 1 1

40 60 120− =

Required time = 120 minQ.45.(A)

1 1

1 4

4 4 1

4 3

2 1

2 3

3 6 2

3 4

1, 7

1 7 8

x

y

x y

x y

x

y

x y

x y

x y

x y

+ =+

⇒ + = +⇒ − = −

+ =+

⇒ + = +⇒ − = −

= =+ = + =

Q.46.(B) Let the length of train be x metre speed = 90 km/hr = 25m/s Distance covered in 60 sec. = 25 × 60 = 1500 meter 1500 = x + x 1500 = 2x x = 750

Q.47.(D) Sale of B in 2011 = 60

78000 780 60100

× = ×

Sale of A in 2013 = 60

68000 680 60100

× = ×

Required ratio = 78: 68 = 39: 34

Q.48.(B) Sale of A = 52

70000 36400100

× =

Total no. of motorcycle sold by B = 81000 Required %

36400

100 44.938% 45%81000

= × = ≈

Q.49.(D) Total no. of motorcycle sold by B

70 60 55 70 63

56000 78000 80000 60000 81000100 100 100 100 100

= × + × + × + × + ×

70 60 55 70 63

56000 78000 80000 60000 81000100 100 100 100 100

= × + × + × + × + ×

= 39200 + 46800 + 44000 + 42000 + 51030 = 223030

Required average 223030

446065

= =

Q.50.(D) Total value of A in 2011

58

72000 41760100

= × =

Total value of A in 2012

75

92000 69000100

= × =

Required % =

69000 41760 27240

100 100 65.229% 65%41760 41760

− × = × = ≈

Q.51.(C) On putting x = – 2 in polynomial x2 + ax + b (– 2)2 + a (– 2) + b = 0 – 2a + b + 4 = 0 2a – b = 4 ---------(I) On putting x = – 2 in the polynomial x2 +bx + a – 2b + a + 4 = 0 a – 2b = – 4 ----------(II) On solving (I) and (II), a = b = 4 So, a : b = 1 : 1 Q.52.(A) a2 – 3a + 1 = 0 On dividing both sides by a, we get

a – 3 + 1

a= 0

a + 1

a = 3

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Now, a5 + 5

1

a = 3 2

3 2

1 1 1a a a

a a a + + − +

= 3 2

1 1 1 1a 3 a a 2 a

a a a a

+ − + + − − +

= {(3)3 – 3 (3)} {(3)2 – 2} – 3 = (27 – 9) × 7 – 3 = 126 – 3 = 123Q.53.(B)

∠ AEB = 90o (AB is a diameter)

In ΔODB,

BD = 2 213 8 105− = BE = 2 105

AE = 676 420− = 16 cm.

AD = 256 105+ = 19 cm.

Q.54.(B)

= 1 1

x y−

Q.55.(D)

o o

o o o o

o oo o

o o

sin 57 cos37tan 57 cot 37 cos57 sin 37

sin 33 cos53tan 33 cot 53cos33 sin 53

++ =+ +

=

o o o o

o o

o o o o

o o

sin 57 sin 37 cos57 cos37cos57 sin 37

sin 33 sin 53 cos33 cos53cos33 sin 53

+

+

=

( )

( )

o o

o o

o o

o o

cos 57 37

cos57 sin 37cos 53 33

cos33 sin 53

−

−

= o o o o

o o o o

cos33 sin 53 sin 57 cos37

cos57 sin 37 cos57 sin 37=

= tan 57o cot 37o

Q.56.(A)

( ) ( )2 2

x cos 3 x sin 1 0θ − + θ − =

x cos θ – 3 = 0 … (I) and x sin θ – 1 = 0 … (II) From (I) and (II), x2 = 4 x = 2

and tan θ = 1

3 θ = 30o

o o

o o

x tan sec 2 tan 30 sec30

x sec tan x sec30 tan 30

θ + θ +=θ + θ +

=

1 22

3 32 1

23 3

× +

× +

= 4

5

Q.57.(D) 480 = 1

2× (2x + 3x) × 12

80 = 5x x = 16 Longer side = 3 × 16 = 48 cm.Q.58.(C) p4 + p2q2 + q4 = 6 p4 + q4 = 6 – p2q2 … (i) again p2 + pq + q2 = 2 p2 + q2 = 2 – pq … (ii) squaring on both side in eq. (ii) p4 + q4 + 2 p2q2 = 4 + p2q2 – 4pq

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MAY 2020 MICAArcelorMittal Nippon Steel India has completed the acquisition of 500 Mega Watt (MW)

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6 – p2q2 + 2 p2q2 = 4 + p2q2 – 4pq 2 = – 4pq pq = – 1/2 Q.59.(D) Distance between lines =

2 2 2 2

c d 22 15 7

10a b 8 6

− −= =+ +

Q.60.(C)

1

2x 53x

+ =

6x2 + 1= 15x

2

5x 5x 5x 1

6x 30x 1 15x 30x 45x 9= = =

+ + +

Q.61.(B) x = 3 3 8 7 4 3+ + −

= ( )2

3 3 8 2 3+ + −

= ( )3 3 8 2 3+ + −

= 3 3 16 8 3+ + −

= 3 19 8 3+ −

= ( )2

3 4 3+ −

= ( )3 4 3+ −

= 4 = 2Q.62.(A)

sin cos4

sin cossin cos 4sin 4cos

3sin 5cos

5tan

3

θ + θ =θ − θθ + θ = θ − θ

θ = θ

θ =

2 2

4 4 5 3sin cos

25 9 25 9

25 9 16 8

34 34 34 17

θ − θ = − + +

= − = =

Q.63.(C) Length of transverse common tangent =

( )221 2d r r− +

= ( )2210 3 3− +

= 2 210 6−

= 8 cm.Q.64.(B) Let a be the first tem and d be the common

difference of given AP 7 T7 = 11 T11

7 (a + 6d) = 11 (a + 10d) 7a + 42d = 11a + 110d 4a + 68d = 0 T18 = a + 17d = 4a + 68d = 0Q.65.(A) 2 (l + b) × h = 448 2 (18 + b) × 8 = 448 18 + b = 28 b = 10Q.66.(A) (p + q + r)2 = p2 + q2 + r2 + 2 (pq + qr + rp) 361 = 133 + 2 (pq + qr + q2) 114 = q (p + q + r) q = 6 Now, p + r = 13 and p2 + r2 = 97 Again, (p – r)2 = p2 + r2 – 2 rp (p – r)2 = 97 – 2 × 36 (p – r)2 = 25 p – r = 5Q.67.(B) 4 – 2 sin2 θ – 5 cos θ = 0 4 – 2 (1 – cos2 θ) – 5 cos θ = 0 4 – 2 + 2 cos2 θ – 5 cos θ = 0 2 cos2 θ – 5 cos θ + 2 = 0 2 cos2 θ – 4 cos θ – cos θ + 2 = 0 2 cos (cos θ – 2) – 1 (cos θ – 2) = 0 (cos θ – 2) (2 cos θ – 1) = 0 cos θ = 2, ½

θ = 60o

sin θ + tan θ = sin 60o + tan 60o

= 3

32

+

= 1

3 12

+

= 3 3

2Q.68.(B)

110

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MICA MAY 2020Yusuffali MA, chairman of the LuLu Group, became the first Indian to receive Saudi

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5x 37

3 2 3 1

2 2 4

− + =

10x 97

6 3 1

2 2 4

− + =

10x 9 3 17

12 2 4

− + =

70x 63 18 1

12 4

− + = 70x – 45 = 3

x = 48/70 = 24/35Q.69.(C)

AQ = AR, BP = BR and CQ = CP Perimeter of the triangle = AB + BC + CA = AR + BR + BP + PC + AQ + CQ = (AR + AQ) + (BP + BR) + (CQ + CP) = 2 × 4.5 + 2 × 6 + 2 × 5.5 = 9 + 12 + 11 = 32 cm.Q.70.(C) T3 = a + 2d = – 13 … (I) T6 = a + 5d = – 4 … (II) From (I) and (II), we get 3d = 9 d = 3 From (I), we get a = – 13 – 6 = – 19 Required Sum = 6 [2 × (– 19) + 11 × 3] = 6 [– 38 + 33] = – 30Q.71.(A) Required coordinates of the point = {(2 × – 3) –

5, 2} = (– 11, 2)Q.72.(D)

3 5 4

5 x 3

+ = −− −

24 = 20 + 4x

4x = 4 x = 1Q.73.(A) Unit digit of 771 + 663 × 365 = 3 + 6 × 3 = 1Q.74.(C)

( )2 2sec tan sec tansec tan 1

tan sec 1 tan sec 1

θ + θ − θ − θθ + θ − =θ − θ + θ − θ +

=( )[ ]sec tan 1 sec tan

tan sec 1

θ + θ − θ + θθ − θ +

= ( )sec tanθ + θ

= 1 sin

cos cos

θ + θ θ

= 1 sin

cos

+ θ θ

= 1 sin 1 sin

cos 1 sin

+ θ − θ × θ − θ

= ( ) ( )2cos cos

cos 1 sin 1 sin

θ θ=θ − θ − θ

Q.75.(D)

1 1 1

n n= +

+l l

(l + n)2 = ln l2 + n2 + 2ln = ln l2 + n2 + ln = 0 l3 – n3 = (l – n) (l2 + n2 + ln) = 0Q.76.(C)

EC = AC and CF = BC

∠ CEA = ∠ CAE = θ (Let)

and ∠ CFB = ∠ CBF = φ (Let) In ∆ DEF,

θ + φ = 180o – 40o = 140o

Now, ∠ ACB = 180o – ( ∠ ACE + ∠ BCF)

= 180o – (180o – θ – θ +180o – φ – φ )

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= 180o – 360o + 2 θ + 2 φ

= 2( θ + φ ) – 180o

= 2 × 140o – 180o = 100o

Q.77.(D) Radius of in circle = 2 A

P

×

A = 22.5 cm2 Volume of prism = Area of base × height

Height = 315

22.5cm. = 14 cm.

Q.78.(A) Radius of the sphere = 5 2 cm. Diameter of the sphere = 10 2 cm. Diagonal of the cube = Diameter of the sphere =

10 2 cm.

Volume of the cube = 3

10 2

2

cm.3

= 1000 cm.3

Q.79.(C)

AB = AC, M is the mid - point of AC

AB + AM = 15 and BC + CM = 6 Let CM = x AM = x BC = 6 – x and AB = 15 – x 15 – x = 2x 3x = 15 x = 5 BC = 6 – 5 = 1 cm. Q.80.(A)

Join QS.

∠ PSQ = ∠ SQR + 36o (exterior angle of ΔSQU)

∠ QSR = ∠ PQS + 24o (exterior angle of ΔTSQ)

∠ PSQ + ∠ QSR = ∠ SQR + 36o + ∠ PQS + 24o

∠ PSR = ∠ PQR + 60o

180o - ∠ PQR = ∠ PQR + 60o

2 ∠ PQR = 120o

∠ PQR = 60o

Q.81.(B)

( )21a 1 3

a+ =

1a 3

a+ =

( )333

1a 3 3 3

a+ = − ×

= 27 – 9 = 18Q.82.(D)

1 1 12

a b c+ + =

On solving this we get, ab + bc + ac = 2abc (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca) 52 = 8 + 2 × 2abc abc = 17/4Q.83.(B) According to the question, Volume of the cuboid = 8 × 6 × 4 = 192 cm.3

Required quantity = 216 – 192 = 24 cm.3

Q.84.(A) x sin 60o. tan 30o – tan2 45o = cosec 60o cot 30o – sec2 45o

3 1 2

x 1 3 22 3 3

⇒ × × − = × −

x = 2Q.85.(C)

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MICA MAY 2020Finance Minister Nirmala Sitharaman said the exercise of consolidation of 10 public sector banks (PSBs) into four is on course and the merger will come into effect from April 1, 2020.

Q.86.(C) PT2 = PA × PB PT2 = 2PT × (2PT – AB) PT2 = 4PT2 – 36 PT 3PT2 = 36 PT PT = 12 Q.87.(A) Let the width of the path be x meters. According to question, (20 + 2x) (14 + 2x) – 20 ×14 = 111 4x2 + 68x – 111 = 0

x = 37

–2 or x =

3

2

Width of path is 1.5 meter.

Q.88.(C) Distance covered in 1 revolution = 222 1.4

7× × =

8.8 m. Distance covered in 40 revolutions = 40 × 8.8 =

352 m. = 0.352 km.

Time = 1

60hr.

Speed = 0.352

160

= 21.12 km/h

Q.89.(A)

Let the radius of the three circles be x, y, z.

x + y = 5, z + y = 7, x + z = 6 x + y + z = 9 x = 9 – 7 x = 2 cm. Q.90.(B) Let the larger number be x and smaller number

be y. Then

3x = 4y + 3 ------- (1) and 7y = 5x + 1 ------- (2) From (1) and (2) x = 25 and y = 18 Required difference = 25 – 18 = 7

Q.91.(D) Volume of cone = ( )219 9 243

3× π × = π cm.3

Volume of sphere = ( )349 972

3× π = π cm.3

Required difference = 972 π – 243 π= 729 π

Percentage of wasted wood = 729100

972

π ×π

= 75%

Q.92.(C) According to the question,

( )2 2 21 12 R h 2 R 12 8π + π = π −

2

1 1R h R 40+ =

21

1

40 Rh

R

−=

Q.93.(D)

Length of the ladder remains same in both the cases.

AC = x + 2 In right angled – triangle ∆ABC, (x + 2)2 = x2 + 82

x2 + 4 + 4x = x2 + 64 4x = 60 x = 15 Q.94.(B)

12 cm.xkm 52

400km 1cm. 2

5x 400 1000km.

2

= =

∴ = × =

Q.95.(B)

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tan 30o = h

PM

PM = 3h

tan 60o = h 120

PM

+

h 120

3PM

+=

h = 60 Height of cloud = 120 m.Q.96.(C) Let height at which balloon is flying is h m.

tan 30o = h

100 h+

1 h

100 h3=

+

( )h 3 1 100− =

h = ( )50 3 1+

Q.97.(A) Required Number = 8.4 × 55 + 54 ×6 = 462 + 324 = 786

Q.98.(D) Required = 360 100

%220

×= 163.64% ≈ 164%

Q.99.(A) Required ratio = (234 + 77) : (126 + 143) = 311 : 269Q.100.(B) Total number of males = 840 × 0.55 + 220 × 0.65

+ 900 × 0.77 + 360 × 0.35 + 450 × 0.56 + 540 × 0.60

= 462 + 143 + 693 + 126 + 252 + 324 = 2000 Total number of females = 840 × 0.45 + 220 ×

0.35 + 900 × 0.23 + 360 × 0.65 + 450 × 0.44 + 540 × 0.40

= 378 + 77 + 207 + 234 + 198 + 216 = 1310 Required difference = 2000 – 1310 = 690

The government permitted NRIs to control up to 100 per cent stake in disinvestment-bound Air India.