Josh Magazine SSC Combined Higher Secondary Exam 2012 Quantitative Aptitude 2

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SSC Combined Higher Secondary Exam 2012 : Quantitative Aptitude

2

SSC Combined Higher Secondary Exam 2012

Quantitative Aptitude

1. A number consists of two digits and the digit in the ten’s place is one third of

the digit in the unit place. If the thrice of the sum of digits is subtracted from

the number, we get the digit at the ten’s place as the result. Find the number.

(a) 26

(b) 62

(c) 39

(d) 13

2. The greatest among the numbers

54

, 76

, 1512

, 83

, 1

(a) 83

(b) 1512

(c) 76

(d) 54

3. A fraction becomes 1

3 when 3 is subtracted from its numerator and 1 is added

to its denominator. If 2 and 4 are respectively added to its numerator and

denominator, it becomes 3

5 Then, the LCM of the numerator and denominator

of the said fraction, must be (a) 33

(b) 44

(c) 66

(d) 77

4. (421 + 422 + 423 + 424) is divisible by

(a) 7

(b) 13

(c) 17

(d) 19


3

5. The ratio of two numbers is 5 : 7 and their H.C.F, is 9. then their L.C.M. is (a) 35

(b) 315

(c) 63

(d) 81

6. A and B can do a piece of work in 10 days. B and C can do it in 12 days. C can do it in 20 days. How long will A take to do it alone? (a) 12

(b) 15

(c) 20

(d) 30

7. A does one-third as much work as B in half of the time taken by B. If together they take 15 days to complete a work, then the time taken by B alone to do it would have been (a) 20

(b) 25

(c) 30

(d) 35

8. A single discount equivalent to discount series 10%, 20% and 30% is

(a) 60%

(b) 50%

(c) 49.6%

(d) 44.6%

9. Two containers have milk and water mixed respectively in the ratio 2 : 3 and 5 : 3. To get a new mixture with ratio of milk to water as 4 : 3, the two types have to be mixed in the ratio (a) 2 : 3

(b) 5 : 3

(c) 4 : 3

(d) 1 : 2


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10. If a shopkeeper marks the price of goods 50% more than their cost price and allows a discount of 30%, what is his gain or loss percent? (a) Gain of 5%

(b) Gain of 10%

(c) Gain of 20%

(d) Loss of 20%

11. The average of three numbers is 30. The largest number is six more than the

twice of the lowest number. The difference between the largest and the

lowest number is 26. Find the number which is neither the largest nor the

lowest.

(a) 20

(b) 24

(c) 30

(d) 46

12. By selling 12 oranges for 40, a man loses 20%. The number of oranges he has to sell for Rs.100, so as to gain 20% is (a) 12

(b) 18

(c) 21

(d) 24

13. The cost price of 250 lemons is equal to the selling price or 200 lemons. Then the profit percent is (a) 10%

(b) 15%

(c) 20%

(d) 25%

14. A man spends 80% of his income. His income increased by 20% and he increased his expenditure by 10%. His savings will then be increased by (a) 33%

(b) 50%

(c) 60%

(d) 75%


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15. 40 litres of salt solution contains 10% salt. How many litres of water must be added so as to get a resultant solution containing 8% salt? (a) 10

(b) 20

(c) 30

(d) 40

16. The current of a stream runs at the rate of 3 km an hour. A bout goes 6 km and comes back to the starting point in 8 hours. The speed of the boat in still water is (a) 12 km/hour

(b) 15 km/hour

(c) 18 km/hour

(d) 21 km/hour

17. On what sun of money will the difference between the simple interest and the compound interest for 2 years at 10% per annum be equal to 15? (a) ̀ 100

(b) ̀ 1000

(c) ` 1500

(d) ̀ 2000

18. A train of length 75 metres running at the speed 108 km/h crosses another

train of length 65 metres which is running at the speed 72 km/h in the same

direction. Find the time (in seconds) taken to cross the train.

(a) 6.5 seconds

(b) 7.5 seconds

(c) 2.4 seconds

(d) 14 seconds

19. If tan θ = 5

12 , then the value of

sin θ + cos θ

tan 2 θ + 2 tan θ + 1 is

(a) 0

(b) 1

(c) 144

289

(d) 144

221


6

20. The value of tan 6°. tan 26°. tan 45°. tan 64°. tan 84° is

(a) 0

(b) 1

(c) 3

(d) 1

3

21. The value of sin 13°. cos 77° + cos 13°. sin 77° is

(a) 1

(b) 0

(c) 3

(d) 1

3

22. If sin θ = 3

5 , then the value of

8 tan θ−3 cot θ

5 sin θ+10 cos θ is

(a) 0

(b) 1

(c) 2

11

(d) 4

13

23. A person is standing at a point M which makes an angle of elevation of 30°

with a tower. He walked 20 metres towards the tower and the angle of

elevation becomes 45°. Find the height of the tower in metres.

(a) 20

(b) 20( 3 + 1)

(c) 10( 3 + 1)

(d) 20( 3 − 1)


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Directions: (Questions No. 74 to 78). The following bar graph shoes the production of fertilizers (in lakh tonnes) by a company, in six consecutive years. Study the graph and answer questions no. 74 to 78.

24. The difference of the average production of fertilizers in the first three years and the average production in the last three years (in lakh tonnes) is (a) 18.33

(b) 20.33

(c) 24.33

(d) 25.33

25. The ratio of the total production of fertilizers in the years 2004, 2006 and 2007 to the total production in the remaining three years is (a) 4 : 5

(b) 2 : 3

(c) 44 : 49

(d) 35 : 44

26. The total production of fertilizers in the years 2004 and 2006 is x% of the total production in the years 2007 and 2009. Then x is equal to (a) 50

(b) 75

(c) 80

(d) 120

5055

7060

8090

0

20

40

60

80

100

2004 2005 2006 2007 2008 2009

Production of Fertilizers


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27. The year in which the production of fertilizers is nearest to the average production of all the six years, is (a) 2005

(b) 2006

(c) 2007

(d) 2008

28. Percentage increase in production of fertilizers for a year with respect to its previous year was maximum in the year (a) 2005

(b) 2006

(c) 2008

(d) 2009


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Directions: (Questions No. 79 to 84). The following bar graph shoes the

production Cost of fertilizers (in Billion $) and Profit (in Billion $) by a company, in

six consecutive years. Study the graph and answer questions no. 79 to 84.

(Use Sales Revenue = Production Cost + Profit)

29. The year in which the production cost of fertilizers is nearest to the average

production cost of all the five years, is

(a) 2002

(b) 2003

(c) 2004

(d) 2005

30. The year in which the profit is nearest to the average profit of all the five

years, is

(a) 2002

(b) 2003

(c) 2004

(d) 2005

60

7075

90

110

15 14

2530

22

0

20

40

60

80

100

120

2001 2002 2003 2004 2005

Production Cost Profit


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31. In which years the profit percentage is the lowest as compare to other years?

(a) 2001 and 2002

(b) 2002 and 2003

(c) 2003 and 2004

(d) 2002 and 2005

32. In which years the profit percentage is the highest as compare to other years?

(a) 2001 and 2002

(b) 2002 and 2003

(c) 2003 and 2004

(d) 2002 and 2005

33. In which year the sales revenue is the highest?

(a) 2002

(b) 2003

(c) 2004

(d) 2005

34. In which year the sales revenue is lowest as compare to other years?

(a) 2001

(b) 2002

(c) 2004

(d) 2003

35. a, b, c, d, e are consecutive even numbers. p, q, r, s, t are consecutive odd numbers. The average of all the numbers is

(a) c + r

2

(b) a + t

2

(c) a + e + p + t

4

(d) 3 c + r

2


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36. Each interior angle of a regular polygon is 135°. The number of sides of the polygon is (a) 6

(b) 7

(c) 8

(d) 9

37. The sum of all the exterior angle of a polygon of n number of sides is

(a) (n – 2)180°

(b) 360°

(c) N × 180°

(d) ∞

38. There is a pyramid on a base which is a regular hexagon of area 50 sq. cm. If the height of the pyramid is 30 cm, then the volume of this pyramid is (a) 80 cm3

(b) 500 cm3

(c) 300 cm3

(d) 1500 cm3

39. Two solid right cones of equal heights h and of radii r1 and r2 are melted and made to from a solid cylinder of radius R and height h. Then the radius of the cylinder is (a) r1 + r2

(b) 1

2 r1

2 + r22

(c) 1

3 r1

2 + r22

(d) r1 + r2

2

40. The ratio of radii of two cylinders is 3 : 4 and the ratio of their heights is 4 : 3. Then the ratio of their volumes will be (a) 3 : 4

(b) 4 : 3

(c) 9 : 16

(d) 16 : 9


12

41. The area of the four walls of a room is 208 m2 and its length is thrice of its breadth. If the height of the room is 13 m, then the area of its floor (in m2) is (a) 12

(b) 13

(c) 16

(d) 208

42. To get the ratio p : q (for p ≠ q), one has to subtract from each term of the ratio x : y, the number

(a) qx − py

q − p

(b) qx + py

q − p

(c) qx + py

q + p

(d) qx − py

q + p

43. The circumcentre of a triangle ABC is O, If BAC = 55° and BCA = 75°, then the value of OAC is (a) 20°

(b) 25°

(c) 30°

(d) 40°

44. Two chords AB and CD of a circle whose centre is O, meet at the point P and AOC = 70°, BOD = 50°, Then the value of BPD is (a) 50°

(b) 60°

(c) 70°

(d) 80°

45. AB = 24 cm and CD = 10 cm are two parallel chords on the same side of the centre or a circle. The distance between them is 7 cm. The radius of the circle is (a) 10 cm

(b) 12 cm

(c) 13 cm

(d) 25 cm


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46. In a triangle ABC, AB = 50 cm, BC = 40 and CA = 30 cm. The area of the

triangle ABC (in cm2) is

(a) 500

(b) 600

(c) 1000

(d) 1500

47. If x2 + y2 − 2x + 1 = 0, then the value of x44 + y47 (a) 0

(b) −1

(c) 2

(d) 1

48. The L. C. M. and H. C. F. of two numbers a and b are 3 and 105 respectively. If a

+ b = 36, then the value of 1

a+

1

b is

(a) 1

(b) 1

6

(c) 12

315

(d) 4

35

49. ̀ 49 have been divided among 150 children. If each girl gets 50 paise and each

boy gets 25 paise, then the number of boys is

(a) 100

(b) 102

(c) 104

(d) 106

50. The value of x in the equation 1

x − 3−

1

x + 5=

1

6 are

(a) 7, 9

(b) −7, 9

(c) −7, −9

(d) 7, −9


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Answers:-

1. (a)

2. (a)

3. (d)

4. (c)

5. (b)

6. (b)

7. (b)

8. (c)

9. (d)

10. (a)

11. (b)

12. (c)

13. (d)

14. (c)

15. (a)

16. (a)

17. (c)

18. (d)

19. (d)

20. (b)

21. (a)

22. (c)

23. (c)

24. (a)

25. (a)

26. (c)

27. (b)

28. (c)

29. (b)

30. (d)

31. (d)

32. (c)

33. (d)

34. (a)

35. (a)

36. (c)

37. (b)

38. (b)

39. (c)

40. (a)

41. (a)

42. (a)

43. (d)

44. (b)

45. (c)

46. (b)

47. (d)

48. (d)

49. (c)

50. (d)

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Josh Magazine SSC Combined Higher Secondary Exam 2012 Quantitative Aptitude 2