ssc cgl tier ii exam solved paper 1-08-2010

8/4/2019 SSC CGL Tier II Exam Solved Paper 1-08-2010

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Solved Paper

1. A General, while arranging his men, who

were 6000 in nu mber, in the form of a square,

found that there w ere 71 men left over. How

many w ere arranged in each row?

(a) 73 (b) 77(c) 87 (d) 93

2. A num ber, wh en d ivided successively by 4,

5 and 6, leaves remainders 2, 3 and 4

respect ively. The least such num ber is

(a) 50 (b) 53

(c) 19 (d) 214

3. A num ber, when d ivided by 296, gives 75 as

the remainder. If the same num ber is divided

by 37 then the remainder w ill be(a) 1 (b) 2

(c) 19 (d) 31

4. The square root of

32(0.75)

0.75 (0.75) 11 0.75

(a) 1 (b) 2

(c) 3 (d) 4

5. The sum an d pr oduct of two num bers are

12 and 35 respectively. The sum of their

reciprocals will be

(a)1

3(b)

1

5(c)

12

35(d)

35

12

6. If2 2

2 2

1 1a b

a b , then the value ofa2 + b2

will be

(a) 1 (b)1

12

(c) 2 (d)1

22

7. If

21

xx

= 3, then

331x x

is equal to

(a) 3 (b) 2

(c) 1 (d) 0

8.0.1 0.1 0.1 0.02 0.02 0.02

0.2 0.2 0.2 0.04 0.04 0.04

is equal to

(a) 0.125 (b) 0.250

(c) 0.500 (d) 0.855

9. If1

xx

= 2, then th e value of100

100

1x

x is

(a) 2 (b) 0

(c) 1 (d) 2

10. Ifx3 + 3x2 + 3x = 7, thenx is equal to

(a) 2 (b) 3 6

(c) 1 (d) 1

11. If2

2xx

= 1, then the v alue of3

3

1x

x is

(a)13

8(b)

11

8(c)

11

8(d)

13

8

12. Th e g rea t es t n u mb er amo n g

3 5 75, 4 , 2, 3 is

(a) 3 4 (b) 7 3

(c) 5 (d) 5 2

SSCCombined Graduate Level TierII Exam

Held on: 01.08.2010

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Solved Paper

13. 2 23 (13.608) (13.392) is equal to

(a) 0.6 (b) 0.06

(c) 1.8 (d) 2.6

14.

1 1 1 1

...1 2 2 3 3 4 99 100

is equa l

to:

(a)1

9900(b)

99

100(c)

100

99(d)

1000

99

15. The sum of all the digits of the numbers from

1 to 100 is

(a) 5050 (b) 903

(c) 901 (d) 900

16. A shopkeeper sells suger in such a way tha t

the selling price of 950g of sugar is the sam e

as the cost price of 1 kg of sugar. What is his

gain per cent?

(a)5

519

(b)1

55

(c) 5 (d)1

419

17. A person bought a hor se and a carriage for

Rs. 20000. Later, he sold the horse at 20%

profit and the carr iage at 10% loss. Thus, he

gained 2% in the whole transaction. The cost

price of the horse w as

(a) Rs. 7200 (b) Rs. 7500

(c) Rs. 8000 (d) Rs. 9000

18. A sells an article to B at 15% profit. B sells it

to C a t 10% loss. If C p ays Rs. 517.50 for it

then A pur chased it at

(a) Rs. 500 (b) Rs. 750(c) Rs. 1000 (d) Rs. 1250

19. An article is sold a t a certai fixed price. By

selling it at2

3of that price, one loses 10%.

The gain per cent on selling it at t he original

pr ice is

(a) 20 (b)1

33

3

(c)200

9(d) 40

20. A sells an ariticle to B for Rs. 45,000 losing

10% in the transaction. B sells it to C at a

price which would have given a profit of

10% to A. By what p er cent d oes B gain?

(a)75

2(b)

100

3(c)

200

9(d)

150

7

21. The cost price of an article is 80% of its

marked price for sale. How much p er cent

does the trad esman gain after allowing a

d iscount of 12% ?

(a) 20 (b) 12

(c) 10 (d) 8

22. A merchant has ann ounced 25% rebate on

prices of ready-made garm ents at the time

of sale. If a pu rchase needs t o have a rebate

of Rs. 400, then how many shirts, each

costing Rs. 320, should he pu rchase?

(a) 10 (b) 7

(c) 6 (d) 5

23. A merchant p urchases a wristwatch for Rs.

450 and fixes its list pr ice in a such a way

that after allowing a discount of 10%, he

earns a p rofit of 20%. Then the list price (in

rup ees) of the wristwatch is

(a) 500 (b) 600

(c) 750 (d) 800

24. A red uction of 10% in the price of tea enables

a d ealer to purchase 25 kg more tea for Rs.

22500. What is the redu ced p rice per kg of

tea?

(a) Rs. 70 (b) Rs. 80

(c) Rs. 90 (d) Rs. 100

25. Ram d onated 4% of his income to a char ity

and dep osited 10% of the rest in a Bank. If

now he has Rs. 8640 left w ith him, then his

income is

(a) Rs. 12,500 (b) Rs. 12,000

(c) Rs. 10,500 (d) Rs. 10,000

26. If the length of a rectangle is increased by

10% and its breadth is decreased by 10%,

then its area

(a) decreases by 1% (b) increases by 1%

(c) decreases by 2%

(d) remains unchanged



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Solved Paper

27. Three spher ical balls of radius 1 cm, 2 cm

and 3 cm are melted to form a single

spherical ball. In the process, the loss of

material is 25%. The rad ius of the new ball

is

(a) 6 cm (b) 5 cm

(c) 3 cm (d) 2 cm

28. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9, then

A : D is equal to

(a) 11 : 17 (b) 8 : 27

(c) 5 : 9 (d) 2 : 9

29. If the length of a rectangle is increased in

the ratio 6 : 7 and its bread th is diminished

in the ratio 5 : 4 then its area will be

diminished in the ratio(a) 17 : 16 (b) 15 : 14

(c) 9 : 8 (d) 8 : 7

30. 7 years ago, the ages (in years) of A and B

were in the ra tio 4 : 5; and 7 years hence they

will be in the ratio 5 : 6. The pr esent age of B

is

(a) 56 years (b) 63 years

(c) 70 years (d) 77 years

31. Two numbers are such that thei rdifference,their sum and their produ ct are

in the r atio of 1 : 7 : 24. The prod uct o f the

num bers is

(a) 24 (b) 36

(c) 48 (d) 60

32. A, B, C are p artners in a business. During a

par ticular year, A received one third of the

profit, B received one fourth of the profit and

C received the remaining Rs. 5000. How

mu ch amount of money d id a receive ?

(a) Rs. 1000 (b) Rs. 3000

(c) Rs. 4000 (d) Rs. 5000

33. Three horses are tether ed at 3 corners of a

triangular plot of land having sides 20m,

30m and 40m each with a rop e of length 7m.

The area (in m2) of the region of this plot,

which can be grazed by the horses, is22

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(a)77

3(b) 75 (c) 77 (d) 80

34. A w ire, when bent in the form of a square,

encloses a region of area 121 cm2. If the same

wire is bent into the form of a circle, then the

area of the circle is22

Use7

(a) 150 cm2 (b) 152 cm2

(c) 154 cm2 (d) 159 cm2

35. The ratio of the ar ea of a sector of a circle to

the ar ea of the circle is 1 : 4. If the area of the

circle is 154 cm2, the per imeter of the sector

is

(a) 20 cm (b) 25 cm

(c) 36 cm (d) 40 cm

36. The length of the d iagonal of a cube is 6 cm.

The volum e of the cube (in cm3) is

(a) 18 3 (b) 24 3

(c) 28 3 (d) 30 3

37. If a spher e of rad ius r is divided into four

identical parts, then the total surface area ofthe four par ts is

(a) 4 r2 square unit (b) 2 r2 square unit(c) 8 r2 square unit (d) 3 r2 square unit

38. A sum of money, deposited at some r ate per

cent per annum of compound interest,

doubles itself in 4 years. In how many years

will it become 16 times of itself at the sam e

rate ?

(a) 16 (b) 12(c) 10 (d) 8

39. What i s the d i f ference between the

compound interest and simple interest on

Rs. 4000 at 5% per ann um for 2 years ?

(a) 10 (b) 11

(c) 20 (d) 100

40. The simp le and compound interests on a

sum of money for 2 year a re Rs. 8400 and

Rs. 8652 respectively. The ra te of interest p er

annum is

(a) 6% (b) 7.5% (c) 9% (d) 4.5%

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41. A man can row against the current three-

fourth of a kilometre in 15 minutes and

returns the same distance in 10 minutes. The

ratio of his speed to that of the current is

(a) 3 : 5 (b) 5 : 3

(c) 1 : 5 (d) 5 : 1

42. Two places A and B are 100 km apart on a

highway. One car star ts from A and another

from B at the same tim e. If the cars travel in

the same d irection at a constant speed, they

meet in 5 hour s. If the cars trav el toward s

each other, they meet in 1 hour. What is the

speed of the car runn ing faster ?

(a) 60 km/ hr. (b) 50 km/ hr.

(c) 40 km/ hr. (d) 32 km/ hr.43. A can comp lete a piece of work in 12 days. B

is 60% more efficient than A . The num ber of

days, that B will take to complete the sam e

work, is

(a) 6 (b)1

72

(c) 8 (d)1

82

44. Two p ipes can fill an emp ty tank separately

in 24 minu tes and 40 minu tes respectivelyand a third pipe can empty 30 gallons of

water per m inute. If all the three pipes are

open, empty tank becomes full in one h our.

The capacity of the tank (in gallons) is

(a) 800 (b) 600

(c) 500 (d) 400

45. A batsman, in his 12th innings, makes a score

of 63 runs and th ereby increases his average

score by 2. The average of his score after 12thinnings is

(a) 41 (b) 42

(c) 34 (d) 35

46. The greatest num ber, that divides 43, 91 and

183 so as to leave the same remainder in

each case, is

(a) 9 (b) 8

(c) 4 (d) 3

47.

7

16 6 7 16 6 7 is equal to

(a)1

2(b)

1

3(c)

1

4(d)

1

5

48. The sum of the areas of the 10 squares, the

lengths of whose sid es are 20 cm, 21 cm, ....

29 cm r espectively is

(a) 6085 cm2 (b) 8555 cm2

(c) 2470 cm2 (d) 11025 cm2

49. The square root of

9.5 0.0085 18.9

0.0017 1.9 2.1

is

(a) 15 (b) 45

(c) 75 (d) 225

50. If 123

xx

= 6, then 132

xx

is equal to

(a) 4 (b) 8

(c) 9 (d) 12

51. If x = 122 1 then the value of 2

2

1x

x

is

(a) 2 (b) 2 2

(c) 2 2 (d) 2

52.3 1 2 2 6 12

1 1 1 1 14 3 5 5 7 13

is

equal to

(a)2

13 (b)1

7 (c)1

6 (d)1

5

53.

3 3

2 2

(0.87) (0.13)

(0.87) (0.13) (0.87) (0.13)

is equal to

(a)1

2(b) 2 (c) 1 (d)

12

2

54. Ifx2 +y2 2x + 6y + 10 = 0, then the va lue of

(x2 +y2) is(a) 4 (b) 6

(c) 8 (d) 10



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55. The largest among th e numbers

7 5, 5 3, 9 7 , 11 9 is

(a) 7 5 (b) 5 3

(c) 9 7 (d) 11 9

56. Ifx1/ 3 +y1/ 3 =z1/ 3, then (x +y z)3 + 27xyz

is equal to

(a) 0 (b) 1

(c) 1 (d) 27

57. If 7 7 7 7.... = (343)y 1

theny is equal to

(a)2

3(b) 1

(c)4

3(d)

3

4

58. Ifa2 = 2, then (a + 1) is equal to

(a) a 1 (b)2

1a

(c)

1

3 2

a

a

(d)

1

3 2

a

a

59. The missing term in the sequence 2, 3, 5, 7,

11, ... 17, 19 is

(a) 16 (b) 15

(c) 14 (d) 13

60. The wrong number in the sequence

(a) 32 (b) 47

(c) 63 (d) 83

61.When the price of a toy was increased by20%, the number of toys sold was decreased

by 15%. What was its effect on the total sales

of the shop?

(a) 2% increase (b) 2% d ecrease

(c) 4% increase (d) 4% d ecrease

62. A person sold a horse at a gain of 15%. Had

he bought it for 25% less an d sold it for Rs.

60 less, he would have m ade a p rofit of 32%.

The cost pr ice of the horse w as(a) Rs. 370 (b) Rs. 372

(c) Rs. 375 (d) Rs. 378

63. A sells an art icle to B at a gain of 25% B sells

it to C at a gain of 20% and C sells it to D at

a ga in of 10%. If D pays Rs. 330 for it, how

mu ch did it cost to A ?

(a) Rs. 200 (b) Rs. 250

(c) Rs. 275 (d) Rs. 290

64. By selling an article for Rs. 21, a man lost

such that the p ercentage loss was equal to

the cost price. The cost priceof the article was

(a) Rs. 30 or Rs. 70 (b) Rs. 35 or Rs. 60

(c) Rs. 45 (d) Rs. 50

65. Half of 100 articles were sold at a p rofit of

20% and the rest at a p rofit of 40%. If all the

articles had been sold a t a pr ofit of 25%, the

total profit would have been Rs. 100 lessthan earlier profit. The cost price of each

article was

(a) Rs. 10 (b) Rs. 15

(c) Rs. 20 (d) Rs. 30

66. The market p rice of a clock is Rs. 3200. It is

to be sold at Rs. 2448 at two successive

discounts. If the first d iscount is 10%, then

the second d iscount is

(a) 5% (b) 10%(c) 15% (d) 20%

67. A dealer marks his goods 30% above his cost

price and then allows 15% discount on it.

What is the cost pr ice of an article on which

he gains Rs. 84 ?

(a) Rs. 800 (b) Rs. 560

(c) Rs. 373.33 (d) Rs. 280

68. A shopkeeper w ishes to give 5% comm ission

on the marked price of an article but alsowants to earn a profit of 10%. If his cost pr ice

is Rs. 95, then th e marked price is

(a) Rs. 100 (b) Rs. 110

(c) Rs. 120 (d) Rs. 130

69. Krishnamu rthy ear ns Rs. 15000 per m onth

and spend s 80% of it. Due to pay rev ision,

his monthly income has increased by 20%,

but d ue to pr ice rise, he has to spend 20%

more. His new savings are(a) Rs. 3400 (b) Rs. 3000

(c) Rs. 4600 (d) Rs. 4000



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70. Two numbers are respectively1

12 %2

an d

25% more than a third number. The first

number is how mu ch per cent of the second

number ?

(a) 90 (b) 87.5(c) 25 (d) 12.5

71. Populat ion of a town increases 2 .5%

annu ally but is decreased by 0.5% every year

due to migrat ion . What wi l l be the

percentage of increase in 2 years?

(a) 5 (b) 4.04

(c) 4 (d) 3.96

72. 72% of the stud ents of a certa in class took

Biology and 44% took Mathematics. If each

student took at least one of Biology or

Mathematics and 40 students tookboth of

these subjects, the total num ber of students

in the class is

(a) 200 (b) 240

(c) 250 (d) 320

73. Rs. 1050 are d ivided amon g A, B and C in

such a w ay that the share of A is 25

of the

combined share of B and C. A will get

(a) Rs. 200 (b) Rs. 300

(c) Rs. 320 (d) Rs. 420

74. The sides of a right-angled triangle forming

right an gle are in the ratio 5 : 12. If the area

of the t riangle is 270 cm2, then the length of

the hypotenuse is

(a) 39 cm (b) 42 cm(c) 45 cm (d) 51 cm

75. Two num bers are in the r atio 5 : 6. If their

H.C.F is 4, then their L.C.M. will be

(a) 90 (b) 96

(c) 120 (d) 150

76. Ifa + b + c = 1 and ab+ bc+ ca=1

3then a : b :

c is(a) 1 : 2 : 2 (b) 2 : 1 : 2

(c) 1 : 1 : 1 (d) 1 : 2 : 1

77. A and B enter into partnership with capitals

in the rat io 5 : 6. At the en d of 8 months A

withd raw s his capital. They recived profits

in the ra tio 5 : 9. Binvested the cap ital for

(a) 6 months (b) 8 months

(c) 10 months (d) 12 months

78. What is the length of the radius of the circum-

circle of the equ ilateral triangle, the length

of whose side is 6 3 cm ?

(a) 6 3 cm (b) 6 cm

(c) 5.4 cm (d) 3 6 cm

79. If the measu re of a diagonal and th e area of

a rectang le are 25 cm and 168 cm 2

respectively, what is the length of the

rectang le ?

(a) 31 cm (b) 24 cm

(c) 17 cm (d) 7 cm

80. The num ber of coins, each of radius 0.75 cm

and thickness 0.2 cm, to be melted to m ake a

right circular cylind er of height 8 cm and

rad ius 3 cm, is

(a) 640 (b) 600 (c) 500 (d) 480

81. If the rad ius of a sphere is increased by 2m,

its surface-area is increased by 704 m2.

What is the rad ius of the original sphere?

22Use

7

(a) 16 m (b) 15 m (c) 14 m (d) 13 m

82. A right circular cylinder is circumscribing a

hemisphere such that their bases arecommon. The ratio of their volum es is

(a) 1 : 3 (b) 1 : 2

(c) 2 : 3 (d) 3 : 4

83. A man invested1

3of his capital a t 7%,

1

4at

8% and the remaining at 10% rate of simple

interest. If his an nualincome from interests

is Rs. 561, the capital invested was(a) Rs. 6000 (b) Rs. 5600

(c) Rs. 6600 (d) Rs. 7200



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84. The compou nd interest on Rs. 6250 at 12%

per annu m for 1 year, comp ounded half-

yearly is

(a) Rs. 772.50 (b) Rs. 772

(c) Rs. 672.50 (d) Rs. 672

85. A sum of money lent at compou nd interest

amou nts to Rs. 1460 in 2 years and to Rs.

1606 in 3 years.The rate of interest per

annum is

(a) 12% (b) 11%

(c) 10.5% (d) 10%

86. If A travels to his school from his house at

the speed of 3 km/ hr. then he reaches the

school 5 minutes late. If he travels at the

speed of 4 km/ hr, he reaches the school 5minutes earlier than school time. The

distance of his school from his house is

(a) 1 km (b) 2 km

(c) 3 km (d) 4km

87. A train travelling with a speed of 60 km/ hr

catches another train travelling in the sam e

direction and then leaves it 120 m behind in

18 seconds. The speed of the second train is

(a) 26 km/ hr (b) 35 km/ hr(c) 36 km/ hr (d) 63 km/ hr

88. A and B together can complete a piece of

work in 12 days an d B and C together in 15

days. If A is twice as good a workman as C,

then in how many days will be alone

complete the same w ork ?

(a) 30 (b) 25

(c) 24 (d) 20

89. 4 men and 6 wom en together can complete

a work in 8 days while 3 men and 7 wom en

together can complete it in 10 days. 20

wom en working together w ill comp lete it in

(a) 36 days (b) 32 days

(c) 24 days (d) 20 days

90. The average of two nu mbers A and B is 20,

that of B and C is 19 and of C and A it is 21.

What is the valu e of A?(a) 24 (b) 22

(c) 20 (d) 18

Directions (91-95): The pie chart given below, shows

the expenditure on various items and savings of a

family during the year 2009. Study the pie chart

and answer these questions.

PERCENTAGE OF MONEY SPENT ON VARIOUS

ITEMS AND SAVINGS BY A FAMILY DURING 2009

Others20%

Savings15%

Food 23% Clothing10%

Educationof Children

12%

Transport5%

Housing10%

91. If the tota l income of the family for the year

2009 was Rs. 1,50,000 then the difference

between the expenditures on housing and

transport was

(a) Rs. 15,000 (b) Rs. 10,000

(c) Rs. 12,000 (d) Rs. 7,50092. Maximum expend iture of the family other

than on food, was on

(a) Housing (b) Clothing

(c) Others

(d) Education of children

93. The savings of the family for the year w ere

equal to the expenditure on

(a) Food (b) H ousing

(c) Education of children

(d) Clothing

94. The percentage of the income which was

spent on clothing, education of child ren and

transport together is

(a) 17 (b) 20

(c) 22 (d) 27

95. If the total income of the family was Rs.

1,50,000 then the money spent on food w as(a) Rs. 20,000 (b) Rs. 23,000

(c) Rs. 30,000 (d) Rs. 34,500


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Directions (96-100): Study the bar diagram and

answer these questions.

1200

1000

800

600

400

200

2009200820072006

300

150200 200

800900

1200

Numberofpersons

Persons killed in industrial accident

Persons killed in coal mines

96. The number of persons killed in coal mines

in 2006 was what p er cent of those killed in

indu strial accidents in that year ?

(a) 4 (b) 25

(c) 36 (d) 300

97. In which year, minimum n umber of persons

were killed in industr ial accidents and coalmines together?

(a) 2006 (b) 2007

(c) 2008 (d) 2009

98. In which year, maximum nu mber of persons

were killed in industrial accidents other than

those killed in coal mines?

(a) 2006 (b) 2007

(c) 2008 (d) 2009

99. In which years, minimum number of persons w ere killed in coal mines other than

those killed in indu strial acciden ts?

(a) 2006 (b) 2007

(c) 2008 (d) 2009

100. In a year, on average, how many persons

were killed in industr ial accidents and coal

mines together ?

(a) 121.25 (b) 1212

(c) 1212.5 (d) 1000

ANSWERS

1. (b) 2. (d) 3. (a) 4. (b) 5. (c)

6. (c) 7. (d) 8. (a) 9. (a) 10. (c)

11. (b) 12. (c) 13. (c) 14. (b) 15. (c)

16.(a)

17.(c)

18.(a)

19.(c)

20.(c)

21. (c) 22. (d) 23. (d) 24. (c) 25. (d)

26. (a) 27. (c) 28. (d) 29. (d) 30. (d)

31. (c) 32. (c) 33. (c) 34. (c) 35. (b)

36. (d) 37. (c) 38. (a) 39. (a) 40. (a)

41. (d) 42. (a) 43. (b) 44. (d) 45. (a)

46. (c) 47. (a) 48. (a) 49. (a) 50. (c)

51. (a) 52. (b) 53. (c) 54. (d) 55. (b)

56. (a) 57. (c) 58. (d) 59. (d) 60. (b)

61. (a) 62. (c) 63. (a) 64. (a) 65. (c)

66. (c) 67. (a) 68. (b) 69. (*) 70. (a)

71. (b) 72. (c) 73. (b) 74. (a) 75. (c)

76. (c) 77. (d) 78. (b) 79. (b) 80. (a)

81. (d) 82. (c) 83. (c) 84. (a) 85. (d)

86. (d) 87. (c) 88. (d) 89. (d) 90. (d)

91. (a) 92. (c) 93. (b) 94. (d) 95. (d)

96. (b) 97. (d) 98. (a) 99. (b) 100. (c)

EXPLANATIONS

1. Nu mber of men arranged in the form of a

square

= 6000 71 = 5929

Nu mber of men arranged in each row

= 5929 = 77

2.4x Remainder5y 2

6z 3

1 4

z = 6 1 + 4 = 10

y = 5 10 + 3 = 53

x = 4 53 + 2 = 214

4.

3

2(0.75) [(0.75) 0.75 1 1]1 0.75


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=3 2 2(0.75) (1 0.75)[(0.75) 0.75 1 1 ]

1 0.75

=3 3 3(0.75) 1 (0.75)

0.25

[(a b)(a2 + ab+ b2) = a3 b3]

=1

1 0.75=

1

0.25=

100

25= 4

Squar e root = 4 = 2

5. x +y = 12 ...(i)

xy = 35 ...(ii)

x y

xy

= 1 1x

= 1235

6.2 2

2 2

1 1a b

a b = 4

2 2

2 2

1 1a b

a b = 4

2 21 1

2 2a ba b

= 4

2 21 1

a ba b

= 0

1

aa

= 0,1

bb

= 0

a = b = +1 a2 + b2 = 1 + 1 = 2.

7.

21

xx

= 3

1

xx

= 3

Now, 3 31xx

=

31 1 1

3 . x x x x x x

= 33 3 3= 3 3 3 3 = 0

8. If 0.1 = 1 then, 0.2 = 2a

and 0.02 = b then , 0.04 = 2b

Expression

=2 2 2 2 2 2

a a a b b b

a a a b b b

=

3 3

3 38 8

a ba b

=

3 3

3 38( )

a ba b

= 18

= 0.125

10. x3 + 3x2 + 3x = 7

x3 + 3x2 + 3x + 1 = 7 + 1 = 8

(x + 1)3 = 23

x + 1 = 2

x = 1

11. 22xx

= 1

1

xx

=1

2...(i)

3

3

1x

x

=

31 1 1

3. . x x x x x x

=

31 1

32 2

=1 3

8 2 =

1 12

8

=

11

8

12. LCM of the orders of the su rds = LCM of 2, 3,

5 and 7 = 2101

25=

105

2105= 1105 2105




10/17

Solved Paper

1

34=

70

2104= 170 2104

1

52=

42

2102= 142 2102

1

73 =30

2103 = 130 2103 The largest nu mber

=1

25= 5

13. Expression

=2 23

(13.608) (13.392)

= 3 (13.608 13.392)(13.608 13.392)

= 3 27 0.216

= 327 216

1000

=

3 6

10

=1.8

16. Profit per cent

=Trueweight Falseweight

100False weight

=1000 950

100950

=100

19=

55

19

17. If the GP of horse be Rs.x, then

CP of car riage = Rs. (20000 x)

120 90

(20000 )100 100

x x

=

102

20000 100

120x + 1800000 90x

= 204000

30x = 2040000 1800000

= 240000

x =240000

30= Rs. 8000

18. If an ar ticle is old to B atx% profit/ loss and

B sells the same to C aty% profit/ loss, then

Cs C.P.

= As CP100100

100 100

x

As CP = Cs CP

100 100100 15 100 10

=100 100

517.50115 90

= Rs. 500

19. Let the C.P. of the ar ticle be Rs. 100.

S.P. of th e ar ticle 2

3= 90

S.P. of the article

=90 3

2

= 135

Profit p er cent a t the original p rice = 35

20. As C.P.

=100

4500090

= Rs. 50000

Bs S.P.

=110

50000100

= Rs. 55000

Bs profit per cent

=10000

10045000

=200

9

21. C.P. of the ar ticle = Rs. 100

Marked p rice




11/17

Solved Paper

=100 100

80

= Rs. 125

SP after the d iscount

=125 88

Rs.

100

= Rs. 110

Gain per cent = 10

23. If the mar ked price of the wrist wa tch be Rs.

x, then

90

100x =

450 120

100

= 540

x =

540 100

90

= Rs. 600

24. Let the original p rice of tea be Rs. x/ kg

New price = Rs.9

/ kg10

x

22500 22500

9

10

x x

= 25

10 1

225009x x

= 25

10 9

225009x

= 25

22500 = 25 9x

x = 2250025 9

= 100

New p rice

=9

10010

= Rs. 90 per kg.

25. Let Rams incom e = Rs. 100.

Donation to char ity = Rs. 4

Amou nt deposited in bank

=96 10

100

= Rs. 9.6

Savings = 100 13.6 = Rs. 86.4

Q Rs. 86.4 = 100

Rs. 8640 =100

864086.4

= Rs. 10000

26. Effect on area

=10 10

10 10 %100

= 1%

Here, nevative sign shows d ecrease.

27. Volume of the new ball

= 3 3 31 2 33 4 ( )4 3

r r r

= (13+ 23 + 33)

= (1 + 8 + 27)

= 36p cubic cm.

34

3r = 36

r3 =36 3

4

= 27

r= 3 27 = 3 cm

30. 7 years ago, As age = 4x years and Bs age =

5x years

4 14

5 14

x

x

=

5

6

25x + 70 = 24x + 84

x = 84 70 = 14

Bs presen t age

= 5x + 7 = 5 14 + 7 = 77 years

32. Total p rofit 1 1

13 4

= 5000

Total p rofit 12 4 312

= 5000

Total profit




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Solved Paper

=5000 12

5

= Rs. 12000

As share = Rs.1

120003

= Rs. 4000

34. Side of the squ are

= 121= 11 cm

Length of the wire = 4 11

= 44 cm

2 r= 44

22

2 7 r = 44

r= 7 cm

Area of circle = r2

=22

7 77

= 154 sq. cm.

36. If the age edfe of the cube bex cm then,

3x = 6

x =6

3= 2 3 cm

Volume of the cube = (edge)3

= 2 3 2 3 2 3

= 24 3 cm3

37. Required total surface area

= 4 r2 + 4 r2

= 8 r2 sq.unit

39. Difference

= Principal

2

100

r

=

25

4000100

= Rs. 10

40. Difference = Rs. (8652 8400) = Rs. 252

Rate =2 Difference

100S.I.

=2 252

1008400

= 6%

43. Ratio of their efficiency

= 100 : 160 = 5 : 8

Ratio of time taken = 8 : 5

Time taken by B

=5

128

=15

2=

17

2days

44. Capacity of the tank =x gallons.

Part of the tank filled in 1 minu te

= 3024 40

x x

60 3024 40

x x =x

24 40 60

x x x = 30

5 3 2

120

x x x= 30

20

x=30 x = 600 gallon s

45. Average of the batsm an up to 11th innings

= 63 12 2 = 39

Required a verage = 39 + 2 = 41

46. Required nu mber

= HCF of (91 43), (183 91) and (183 43)

= HCF of 48, 92 and 140 = 4

47. Expression

=7

16 6 7 16 6 7

=7

9 7 2 3 7 9 7 2 3 7

=7

(3 7 ) (3 7 )




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Solved Paper

=7

3 7 3 7 =

1

2

48. Required su m = 202 + 212 + ... + 292

= (12 + 22 + ... + 292) (12 + 22 + ... + 192)

= 29(29 1)(2 29 1) 19(19 1)(2 19 1)6 6

2 2 2 ( 1)(2 1)1 2 ...

6

n n nn

Q

= 8555 2470

= 6085 sq.cm.

49. Expression

=9.5 0.0085 18.9

0.0017 1.9 2.1

= 225

Required square root

= 225 = 15

51. x = 122 1 x 2 = 2 1

x2 =1

2 1=

1 2 1

2 1 2 1

= 2 1

21

x=

2 1

2

2

1x

x = 2 1 2 1 = 2

52. Expression

=3 4 5 3 13 1

4 3 3 5 7 13 =

1

7

53. If 0.87 = a and 0.13 = b then,

Expression =

3 3

2 2

a b

a b ab

=

2 2

2 2

( )( )a b a b ab

a b ab

= a + b = 0.87 + 0.13 = 1

54. x2 2x +y2 + 6y + 10 = 0

x2

2x + 1 +y2

+ 6y + 9 = 0 (x 1)2 + (y + 3)2 = 0

=x 1 = 0 x = 1

and,y + 3 = 0 y = 3

x2 +y2 = 1 + 9 = 10

55. 7 5 = 7 5 7 5

7 5

=2

7 5

Similarly,

5 3 =2

5 3

9 7=

2

9 7

11 9 =2

11 9

Largest number = 5 3

because its denominator is the smallest.

56.1 1

3 3x y =1

3z

Cubing both sides, we have,

3 31 1 1 1 1 1

3 3 3 3 3 33. . x y x y x y

=z

x +y + 3.1 1 1

3 3 33. . .x y x y z =z

(x +y z) =1 1 1

3 3 33. . . x y z

p g p



14/17

Solved Paper

Cubing again,

(x +y z)3 = 27xyz

(x +y z)3 + 27xyz = 0

57. Let x = 7 7 7 7....

On squar ing both sides,

x2 = 7x3

x2 7x = 0 x(x 7) = 0

x = 7

7 = (73) y 1 = 73y 3

3y 3 = 1

3y = 4

y = 43

58. a2 = 2

a = 2

a + 1 = 2 1

From alternat ive (4)

13 2a

a

= 2 1

3 2 2

=2 1 3 2 2

3 2 2 3 2 2

=3 2 3 4 2 2

9 8

= 1 2

59. It is sequence of first p rime numbers.

60. 8 + 5 = 13

13 + 8 = 21

21 + 11 = 32

32 + 14 = 46 47

46 + 17 = 63

61. Effect on sale

=

20 15

20 15 %100

= 2% increase

62. If the CP of horse be Rs. x

then its SP =115

100x

New CP =3

Rs.

4

x

115

60100

x

=3 132

4 100x =

99

100

x

115 99

100 100

x x = 60

16

100

x= 60

x =60 100

16

= Rs. 375

63. As CP =100 100 100

330125 120 110

= Rs. 200

64. If the CP of art icle be Rs. x, then

21100

x

x

=x3

x2 100x + 2100 = 0

x2 70x 30x + 2100 = 0

x (x 70) 30 (x 70) = 0

(x 30) (x 70) = 0 x = Rs. 30 or Rs. 70

65. Let the CP of each article be Rs.x.

5 120 50 140 100 125

100 100 100

x x x = 100

60x + 70x 125x = 100

5x = 100

x =100

5= Rs. 20

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Solved Paper

67. CP of art icle = Rs.

Marked p rice

=130

100

x= Rs.

13

10

x

S.P.

=13 85

10 100

x = Rs.

221

200

x

221

200

xx = 84

221

200

x= 84

x =84 200

21

=Rs. 800

68. Marked price = Rs. . then

95

100

x =

95 110

100

x = Rs. 11010

69. (*) Initial expenditu re of Krishnamu rthy

=80

15000100

= Rs. 12000

New income

=15000 120

100

= Rs. 18000

New expenditure

=12000 120

100

= Rs. 14400

New savings = 18000 14400

= Rs. 3600

Note: It is not an answ er choice.

70. First num ber

=25

1002

=225

2

Second nu mber = 125

Required percentage

=

225

1002 125 = 90

71. Percentage of increase

=2 2

2 2 %100

= 4.04%

72. Percentage of students opting for both

subjects

= 72 + 44 100 = 16

If the total number of students bex, then

16

100

x = 40 x =

4000

16= 250

73. A : B + C = 2 : 5

As share =2

1050

7

= Rs. 300

75. Num bers = 5x and 6x

HCF =x = 4

LCM = 5 6 x

= 5 6 4 = 120

76. a + b + c = 1,

ab+ bc+ ca=1

3

a2 + b2 + c2

= (a + b + c)2 2 (ab+ bc+ ca)

=2

13

=1

3

Clearly, a = b = c =1

3

a : b : c = 1 : 1 : 177. If B invested fory months. then

5 8

6

=

5

9

y = 12 months.

79. l2 + b2 = 625 ...(i)

lb = 168 ...(ii)

(l + b)2

= l2

+ b2

+ 2lb= 625 + 2 168 = 961

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16/17

Solved Paper

l + b = 961 = 31 ...(iii)

(l + b)2 = l2 + b2 2lb

= 625 168 2 = 289

l b = 289 = 17 ...(iv)

From equ ations (iii) and (iv),2l = 48

l =48

2= 24 cm

80. Volum e of the cylind er = r2h

= 32 8 = 72 cm3

Volum e of one coin

= (0.75)

2

0.2 Nu mber of coins

=72

0.75 0.75 0.2

= 640

81. 4 (r+ 2)2 4 r2 = 704

(r+ 2)2 r2 =704

4

r2

+ 4r+ 4 r2

=704 7

4 22

= 56

4r= 56 4 = 52

r= 13 metre

82. Required r atio = Volume of hemi-sphere :

Volum e of cyliner

= 323

r : r3 = 2 : 3

84. T = 2 half years

Rate = 6%

= CI =

2

P 1 1100

r

=266250 1 1

100

= 6250 0.1236 = Rs. 772.5

85. 1460 =

2

P 1100

R

...(i)

1606 =

3

P 1 100

R

...(ii)

Dividing equation (ii) by (i)

1100

R =

1606

1460

R

100=

1606 1460

1460

=1461460

=1

10

86. If the d istance between the school and hom e

bex km, then

3 4

x x =

10

60

12

x=

1

6

x =

112

6

= 2 km

87. 60 kmp h =60 5

m / sec18

=50

m / sec3

If the speed of second train bex m/ sec, then

503

x = 12018

= 203

x =50 20

3 3 = 10 m/ sec

=10 18

kmph5

= 36 kmp h

89. 8 4m + 6w 8

10 3m + 7 10w

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17/17

Solved Paper

2m 22w

1m 11w

4m + 6w = 50w

M1D

1= M

2D

2

50 8 = 20 D2

D2

=50 8

20

= 20 days

90. A + B = 40

B + C = 38

C + A = 42

On add ing,

2(A + B + C) = 40 + 38 + 42 = 120

A + B + C = 60 A = (A + B + C) (B + C)

= 60 38 = 22

91. Expenditure on housing and transport

=10

150000100

= Rs. 15000

92. It is obvious from the p ie char t.

Food 23%, Others 20%

93. Housing 15%

Savings 15%

94. Required percentage

= 10 + 12 + 5

= 27%

95. Expenditur e on food

=

150000 23

Rs. 100

= Rs. 34500

96. Required percentage

=300

1001200

= 25

97. Nu mber of persons killed in 2009

= 800 + 200 = 1000

98. It is obvious from the bar d iagram.

Required num ber of the dead = 1200

99. It is obvious from the bar d iagram.

Required n umber of the dead = 150

100. Required average

=1500 1050 1300 1000

4

=4850

4= 1212.5

ssc cgl tier ii exam solved paper 1-08-2010

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