SSC Previous Year Question Paper SOLVED PAPER SSC COMBINED GRADUATE LEVE PRELIM EXАM

1. A General, while arranging his men, who were 6000 in number, in the form of a square, found that there were 71 men left over. How many were arranged in each row?
(a) 73 (b) 77 (c) 87 (d) 93

2. A number, when divided successively by 4, 5 and 6, leaves remainders 2, 3 and 4 respectively. The least such number is
(a) 50 (b) 53 (c) 19 (d) 214

3. A number, when divided by 296, gives 75 as the remainder. If the same number is divided by 37 then the remainder will be
(a) 1 (b) 2 (c) 19 (d) 31

4. The square root of

5. The sum and product of two numbers 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. If a² b² 1/a² 1/b² , then the value of a² + b² will be
(a) 1 (b) 1½ (c) 2 (d) 2½

7. If (x 1/x⁴ = 3 , then
(x³ 1/x³)
(a) 3 (b) 2 (c) 1 (d) 0

8. 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. If x 1/x = 2 , then the value of x¹⁰⁰ 1/x¹⁰⁰ is
(a) 2 (b) 0 (c) 1 (d) -2

10. If x³ + 3x² + 3x = 7 , then x is equal to
(a) 2 (b) ³√6 (c) 1 (d) -1

11. If 2x 2/x = 1 , then the value of x³ 1/x³ is
(a) 13/8 (b) 11/8 (c) 11/8 (d) 13/8

12. The greatest number among √5, ³√4, ³√2, ³√3 is
(a) ³√4 (b) ³√3 (c) √5 (d) ⁵√2

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13. ³√(13.608)² (13.392) is equal to
(a) 0.6 (b) 0.06 (c) 1.8 (d) 2.6

14. 1/1 1/2 1/2 1/3 1/4 … 1/99 1/100 is equal 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 sugar in such a way that the selling price of 950g of sugar is the same as the cost price of 1 kg of sugar. What is his gain per cent?
(a) 5/19 (b) 5/1 (c) 5 (d) 4/19

17. A person bought a horse and a carriage for Rs. 20000. Later, he sold the horse at 20% profit and the carriage at 10% loss. Thus, he gained 2% in the whole transaction. The cost price of the horse was
(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 at 10% loss. If C pays Rs. 517.50 for it then A purchased it at
(a) Rs. 500 (b) Rs. 750 (c) Rs. 1000 (d) Rs. 1250

19. An article is sold at a certain fixed price. By selling it at 2/3 of that price, one loses 10% . The gain per cent on selling it at the original price is
(a) 20 (b) 33/3 (c) 200/9 (d) 40

20. A sells an article 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 per cent does 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 per cent does the tradesman gain after allowing a discount of 12% ?
(a) 20 (b) 12 (c) 10 (d) 8

22. A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchase needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
(a) 10 (b) 7 (c) 6 (d) 5

23. A merchant purchases a wristwatch for Rs. 450 and fixes its list price in a such a way that after allowing a discount of 10% , he earns a profit of 20% . Then the list price (in rupees) of the wristwatch is
(a) 500 (b) 600 (c) 750 (d) 800

24. A reduction of 10% in the price of tea enables a dealer to purchase 25kg more tea for Rs. 22500. What is the reduced price per kg of tea?
(a) Rs. 70 (b) Rs. 80 (c) Rs. 90 (d) Rs. 100

25. Ram donated 4% of his income to a charity and deposited 10% of the rest in a Bank. If now he has Rs. 8640 left with 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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27. Three spherical balls of radius 1cm, 2cm and 3cm are melted to form a single spherical ball. In the process, the loss of material is 25% . The radius of the new ball is
(a) 6cm (b) 5cm (c) 3cm (d) 2cm

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 breadth 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 ratio 4:5 and 7 years hence they will be in the ratio 5:6 . The present age of B is
(a) 56 years (b) 63 years (c) 70 years (d) 77 years

31. Two numbers are such that their difference, their sum and their product are in the ratio of 1:7:24 . The product of the numbers is
(a) 24 (b) 36 (c) 48 (d) 60

32. A, B, C are partners in a business. During a particular year, A received one third of the profit, B received one fourth of the profit and C received the remaining Rs. 5000. How much amount of money did a receive?
(a) Rs. 1000 (b) Rs. 3000 (c) Rs. 4000 (d) Rs. 5000

33. Three horses are tethered at 3 corners of a triangular plot of land having sides 20m, 30m and 40m each with a rope of length 7m. The area (in m²) of the region of this plot, which can be grazed by the horses, is (Use 22/7)
(a) 77/3 (b) 75 (c) 77 (d) 80

34. A wire, when bent in the form of a square, encloses a region of area 121cm². If the same wire is bent into the form of a circle, then the area of the circle is (Use 22/7)
(a) 150cm² (b) 152cm² (c) 154cm² (d) 159cm²

35. The ratio of the area of a sector of a circle to the area of the circle is 1:4 . If the area of the circle is 154cm², the perimeter of the sector is
(a) 20cm (b) 25cm (c) 36cm (d) 40cm

36. The length of the diagonal of a cube is 6cm. The volume of the cube (in cm³) is
(a) 18√3 (b) 24√3 (c) 28√3 (d) 30√3

37. If a sphere of radius r is divided into four identical parts, then the total surface area of the four parts is
(a) 4r² square unit (b) 2r² square unit (c) 8r² square unit (d) 3r² square unit

38. A sum of money, deposited at some rate 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 same rate?
(a) 16 (b) 12 (c) 10 (d) 8

39. What is the difference between the compound interest and simple interest on Rs. 4000 at 5% per annum for 2 years?
(a) 10 (b) 11 (c) 20 (d) 100

40. The simple and compound interests on a sum of money for 2 year are Rs. 8400 and Rs. 8652 respectively. The rate of interest per annum is
(a) 6% (b) 7.5% (c) 9% (d) 4.5%

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41. A man can row against the current threefourth 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 100km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at a constant speed, they meet in 5 hours. If the cars travel towards each other, they meet in 1 hour. What is the speed of the car running faster?
(a) 60km/hr (b) 50km/hr (c) 40km/hr (d) 32km/hr

43. A can complete a piece of work in 12 days. B is 60% more efficient than A. The number of days, that B will take to complete the same work, is
(a) 6 (b) 7½ (c) 8 (d) 8½

44. Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all the three pipes are open, empty tank becomes full in one hour. 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 thereby increases his average score by 2. The average of his score after 12th innings is
(a) 41 (b) 42 (c) 34 (d) 35

46. The greatest number, 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 sides are 20cm, 21cm, … 29cm respectively is
(a) 6085cm² (b) 8555cm² (c) 2470cm² (d) 11025cm²

49. The square root of 9.5/0.0017 0.0085/1.9 18.9/2.1 is
(a) 15 (b) 45 (c) 75 (d) 225

50. If 2x 1/3x = 6 , then 3x 1/2x is equal to
(a) 4 (b) 8 (c) 9 (d) 12

51. If x = √2 1½ then the value of (x² 1/x²) is
(a) 2 (b) 2√2 (c) 2√2 (d) 2

52. 3/4 (1 1/3 (1 2/5 (1 2/5 (1 6/7 (1 12/13) is equal to
(a) 2/13 (b) 1/7 (c) 1/6 (d) 1/5

53. (0.87)³/(0.13)² (0.13)³/(0.87) is equal to
(a) 1/2 (b) 2 (c) 1 (d) 2½

54. If x² +y² -2x +6y +10 = 0 , then the value of (x² +y²) is
(a) 4 (b) 6 (c) 8 (d) 10

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55. The largest among the numbers √7 √5, √5 √3, √9 √7, √11 √9 is
(a) √7 √5 (b) √5 √3 (c) √9 √7 (d) √11 √9

56. If x^(1/3) + y^(1/3) = z^(1/3) , then (x + y - z)³ + 27xyz is equal to
(a) 0 (b) 1 (c) -1 (d) 27

57. If √7√7√7√7√7√7√7√8 = (343)^(y-1) then y is equal to
(a) 2/3 (b) 1 (c) 4/3 (d) 3/4

58. If a² = 2 , then (a + 1) is equal to
(a) a - 1 (b) 2/(a - 1) (c) a/3 1/2a (d) a/3 1/2a

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 by 20% , 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% decrease (c) 4% increase (d) 4% decrease

62. A person sold a horse at a gain of 15% . Had he bought it for 25% less and sold it for Rs. 60 less, he would have made a profit of 32% . The cost price of the horse was
(a) Rs. 370 (b) Rs. 372 (c) Rs. 375 (d) Rs. 378

63. A sells an article 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 gain of 10% . If D pays Rs. 330 for it, how much 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 percentage loss was equal to the cost price. The cost price of 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 profit of 20% and the rest at a profit of 40% . If all the articles had been sold at a profit of 25% , the total profit would have been Rs. 100 less than earlier profit. The cost price of each article was
(a) Rs. 10 (b) Rs. 15 (c) Rs. 20 (d) Rs. 30

66. The market price of a clock is Rs. 3200. It is to be sold at Rs. 2448 at two successive discounts. If the first discount is 10% , then the second discount 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 price 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 wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10% . If his cost price is Rs. 95, then the marked price is
(a) Rs. 100 (b) Rs. 110 (c) Rs. 120 (d) Rs. 130

69. Krishnamurthy earns Rs. 15000 per month and spends 80% of it. Due to pay revision, his monthly income has increased by 20% , but due to price 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 respectively 12½% and 25% more than a third number. The first number is how much per cent of the second number?
(a) 90 (b) 87.5 (c) 25 (d) 12.5

71. Population of a town increases 2.5% annually but is decreased by 0.5% every year due to migration. What will be the percentage of increase in 2 years?
(a) 5 (b) 4.04 (c) 4 (d) 3.96

72. 72% of the students of a certain class took Biology and 44% took Mathematics. If each student took at least one of Biology or Mathematics and 40 students took both of these subjects, the total number of students in the class is
(a) 200 (b) 240 (c) 250 (d) 320

73. Rs. 1050 are divided among A, B and C in such a way that the share of A is 2/5 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 angle are in the ratio 5:12. If the area of the triangle is 270cm² , then the length of the hypotenuse is
(a) 39cm (b) 42cm (c) 45cm (d) 51cm

75. Two numbers are in the ratio 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. If a + b + c = 1 and ab + bc + ca = 1/3 then 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 ratio 5:6. At the end of 8 months A withdraws his capital. They received profits in the ratio 5:9. B invested the capital for
(a) 6 months (b) 8 months (c) 10 months (d) 12 months

78. What is the length of the radius of the circumcircle of the equilateral triangle, the length of whose side is 6√3 cm ?
(a) 6√3 cm (b) 6cm (c) 5.4cm (d) 3√6 cm

79. If the measure of a diagonal and the area of a rectangle are 25cm and 168cm² respectively, what is the length of the rectangle?
(a) 31cm (b) 24cm (c) 17cm (d) 7cm

80. The number of coins, each of radius 0.75cm and thickness 0.2cm , to be melted to make a right circular cylinder of height 8cm and radius 3cm , is
(a) 640 (b) 600 (c) 500 (d) 480

81. If the radius of a sphere is increased by 2m its surface-area is increased by 704m² . What is the radius of the original sphere? (Use 22/7)
(a) 16m (b) 15m (c) 14m (d) 13m

82. A right circular cylinder is circumscribing a hemisphere such that their bases are common. The ratio of their volumes is
(a) 1:3 (b) 1:2 (c) 2:3 (d) 3:4

83. A man invested 1/3 of his capital at 7% , 1/4 at 8% and the remaining at 10% rate of simple interest. If his annual income 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 compound interest on Rs. 6250 at 12% per annum for 1 year, compounded half- yearly is
(a) Rs. 772.50 (b) Rs. 772 (c) Rs. 672.50 (d) Rs. 672

85. A sum of money lent at compound interest amounts 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 5 minutes earlier than school time. The distance of his school from his house is
(a) 1 km (b) 2 km (c) 3 km (d) 4 km

87. A train travelling with a speed of 60 km/hr catches another train travelling in the same 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 and 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 work?
(a) 30 (b) 25 (c) 24 (d) 20

89. 4 men and 6 women together can complete a work in 8 days while 3 men and 7 women together can complete it in 10 days. 20 women working together will complete it in
(a) 36 days (b) 32 days (c) 24 days (d) 20 days

90. The average of two numbers A and B is 20, that of B and C is 19 and of C and A it is 21. What is the value 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

91. If the total 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. 7,500

92. Maximum expenditure 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 were equal to the expenditure on
(a) Food (b) Housing (c) Education of children (d) Clothing

94. The percentage of the income which was spent on clothing, education of children 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 was
(a) Rs. 20,000 (b) Rs. 23,000 (c) Rs. 30,000 (d) Rs. 34,500

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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)

96. The number of persons killed in coal mines in 2006 was what per cent of those killed in industrial accidents in that year ?
(a) 4 (b) 25 (c) 36 (d) 300

97. In which year, minimum number of persons were killed in industrial accidents and coal mines together?
(a) 2006 (b) 2007 (c) 2008 (d) 2009

98. In which year, maximum number 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 were killed in coal mines other than those killed in industrial accidents?
(a) 2006 (b) 2007 (c) 2008 (d) 2009

100. In a year, on average, how many persons were killed in industrial accidents and coal mines together?
(a) 121.25 (b) 1212 (c) 1212.5 (d) 1000

EXPLANATIONS Solution 

1. Number of men arranged in the form of a square = 6000 - 71 = 5929 Number of men arranged in each row = √5929 = 77

2. 4x Remainder
5y - 2
6z - 3
1 - 4
z = 6×1 + 4 = 10
y = 5×10 + 3 = 53
x = 4×53 + 2 = 214

4. (0.75)³/1.0.75 [(0.75)² 0.75 1 1]

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= (0.75)³ (1 0.75)[(0.75)² 0.75 1 1²] / 1 0.75
= (0.75)³ 1³ (0.75)³ / 0.25
[(a - b)(a² + ab + b²) = a³ - b³]
= 1/1 0.75 = 1/0.25 = 100/25 = 4
Square root = √4 = 2

5. x + y = 12 …(i)
xy = 35 …(ii)
x/xy y/xy = 1/y 1/x = 12/35

6. a² b² 1/a² 1/b² = 4
a² 1/a² b² 1/b² = 4
(a 1/a)² 2 (b 1/b)² 2 = 4
(a 1/a)² (b 1/b)² = 0
a 1/a = 0, b 1/b = 0
a = b = ±1
a² + b² = 1 + 1 = 2

7. (x 1/x)² = 3
x 1/x = √3
Now, x³ 1/x³
= (x 1/x)³ 3x.1/x(x 1/x)
= (√3)³ 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 = a a a b b b / 2a 2a 2a 2b 2b 2b
= a³ b³ / 8a³ 8b³ = a³ b³ / 8(a³ b³) = 1/8 = 0.125

10. x³ + 3x² + 3x = 7
x³ + 3x² + 3x + 1 = 7 + 1 = 8
(x + 1)³ = 2³
x + 1 = 2
x = 1

11. 2x 2/x = 1
x 1/x = 1/2 …(i)
x³ 1/x³
= (x 1/x)³ 3x.1/x(x 1/x)
= (1/2)³ 3 1/2
= 1/8 3/2 = 1 12/8 = 11/8

12. LCM of the orders of the surds = LCM of 2, 3, 5 and 7 = 210
5^(1/2) = 5^(105/210) = ⁵√(5^105) … etc.
The largest number = 5^(1/2) = √5

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13. Expression
= ∛(13.608)² (13.392)²
= ∛(13.608 13.392)(13.608 13.392)
= ∛27 0.216
= ∛(27 216 / 1000)
= 3 6 / 10 = 1.8

16. Profit per cent
= True weight - False weight / False weight × 100
= 1000 - 950 / 950 × 100
= 100/19 = 5 5/19

17. If the CP of horse be Rs. x, then
CP of carriage = Rs. (20000 - x)
x 120/100 (20000 x) 90/100
= 20000 102/100
120x + 1800000 - 90x
= 2040000
30x = 2040000 - 1800000
= 240000
x = 240000/30 = Rs. 8000

18. If an article is old to B at x% profit/loss and B sells the same to C at y% profit/loss, then C's C.P.
= A's CP (100 + x/100) (100 + y/100)
A's CP = C's CP / (100 + x/100) (100 + y/100)
= 517.50 × (100/115) × (100/90) = Rs. 500

19. Let the C.P. of the article be Rs. 100.
S.P. of the article × 2/3 = 90
S.P. of the article = 90 × 3/2 = 135
Profit per cent at the original price = 35

20. A's C.P. = 45000 × 100/90 = Rs. 50000
B's S.P. = 50000 × 110/100 = Rs. 55000
B's profit per cent = 10000/45000 × 100 = 200/9

21. C.P. of the article = Rs. 100
Marked price = 100 × 100/80 = Rs. 125
SP after the discount = Rs. (125 × 88/100) = 110
Gain per cent = 10

23. If the marked price of the wrist watch be Rs. x, then
90/100 × x = 450 × 120/100
x = 540 × 100/90 = Rs. 600

24. Let the original price of tea be Rs. x/kg
New price = Rs. 9x/10
22500/(9x/10) - 22500/x = 25
22500 × 10/9x - 22500/x = 25
New price = 9/10 × 100 = Rs. 90 per kg.

25. Let Ram's income = Rs. 100.
Donation to charity = Rs. 4
Amount deposited in bank = 96 × 10/100 = Rs. 9.6

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= 5000 × 12/5 = Rs. 12000
A's share = Rs. (1/3 × 12000) = Rs. 4000

34. Side of the square = √121 = 11 cm
Length of the wire = 4 × 11 = 44 cm
2 r = 44
2 22/7 r = 44
r = 7 cm
Area of circle = r²
= 22/7 7 7
= 154 sq. cm.

36. If the age edge of the cube be x 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 (r/100)² = 4000 (5/100)² = Rs. 10

40. Difference = Rs. (8652 - 8400) = Rs. 252
Rate = 2 Difference / S.I. × 100
= 2 252 / 8400 × 100 = 6%

43. Ratio of their efficiency
= 100 : 160 = 5 : 8
Ratio of time taken = 8 : 5
Time taken by B
= 12 5/8 = 15/2 = 7½ days

44. Capacity of the tank = x gallons.
Part of the tank filled in 1 minute
= x/24 x/40 30
60(x/24 x/40 30) = x
x/24 x/40 x/60 = 30
5x 3x 2x / 120 = 30
x/20 = 30 ⇒ x = 600 gallons

45. Average of the batsman upto 11th innings
= 63 - 12 × 2 = 39
Required average = 39 + 2 = 41

46. Required number
= 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)

===== Page 12 =====

48. Required sum
= 20² + 21² + … + 29²
= (1² + 2² + … + 29²) - (1² + 2² + … + 19²)
= 29(29 1)(2 29 1)/6 19(19 1)(2 19 1)/6
Q1² 2² … n² n(n 1)(2n 1)/6
= 8555 - 2470
= 6085 sq.cm.

49. Expression
9.5/0.0017 0.0085/1.9 18.9/2.1
= 225
Required square root
= √225 = 15

51. x = √2 1½
x - 2 = √2 1
x² = 1/√2 1 = 1/√2 1 √2 1/√2 1
= √2 1
1/x² = √2 1
x² 1/x² = √2 1 √2 1 = 2

52. Expression
3/4 4/3 5/3 3/5 13/7 1/13 = 1/7

53. If 0.87 = a and 0.13 = b then,
Expression = a³/a² b³/b² a b/a b
= (a b)(a² b² ab)/a² b² 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. x^(1/3) y^(1/3) = z^(1/3)
Cubing both sides, we have,
(x^(1/3))³ (y^(1/3))³ 1/3x^(1/3).y^(1/3)(x^(1/3) y^(1/3))³ = z
x + y + 3.x^(1/3).y^(1/3).z^(1/3) = z
(x + y - z) = 3.x^(1/3).y^(1/3).z^(1/3)

===== Page 13 =====

62. If the CP of horse be Rs. x then its SP = 115/100 x
New CP = Rs. (3/4 115x/100 60)
3/4 132/100 = 99x/100
115x/100 99x/100 = 60
16x/100 = 60
x = 60 100/16 = Rs. 200

64. If the CP of article be Rs. x, then
x 21/100 = 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.
5x 120/100 50x 140/100 100x 125/100
60x + 70x - 125x = 100
5x = 100
x = 100/5 = Rs. 20

===== Page 14 =====

67. CP of article = Rs. x
Marked price = 130x/100 = Rs. 13x/10
S.P. = 13x/10 85/100 = Rs. 221x/200
221x/200 x = 84
221x/200 = 84
x = 84/21 = Rs. 800

68. Marked price = Rs. x, then
x 95/100 = 95 110/100
x = Rs. 110

69. (*) Initial expenditure of Krishnamurthy
= 15000 80/100 = 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 answer choice.

70. First number = 100 25/2 = 225/2
Second number = 125
Required percentage = 225/2 125 100 = 90

71. Percentage of increase
= (2 2 2/100 2/4)% = 4.04%

72. Percentage of students opting for both subjects
= 72 + 44 - 100 = 16
If the total number of students = x, then
x 16/100 = 40 x = 4000/16 = 250

73. A : B + C = 2 : 5
A's share = 2/7 1050 = Rs. 300

75. Numbers = 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)
= 1 2/3 = 1/3
Clearly, a = b = c = 1/3
a:b:c = 1:1:1

77. If B invested for y months, then
5/6 8/y = 5/9
y = 12 months.

79. l² + b² = 625 …(i)
lb = 168 …(ii)
(l + b)² = l² + b² + 2lb
= 625 + 2 168 = 961
l + b = √961 = 31 …(iii)
(l - b)² = l² + b² - 2lb
= 625 - 168 2 = 289
l - b = √289 = 17 …(iv)
From equations (iii) and (iv),
2l = 48
l = 48/2 = 24cm

===== Page 15 =====

80. Volume of the cylinder = r²h
= 3² 8 = 72 cm³
Volume of one coin = (0.75)² 0.2
Number of coins = 72 / (0.75 0.75 0.2) = 640

81. 4 (r + 2)² - 4 r² = 704
(r + 2)² - r² = 704/4 7/22 = 56
r² + 4r + 4 - r² = 56
4r = 56 - 4 = 52
r = 13 metre

82. Required ratio = Volume of hemisphere : Volume of cylinder
= 2/3 r³ : r³ = 2 : 3

84. T = 2 half years
Rate = 6%
CI = P[(1 r/100)^T 1]
= 6250[(1 6/100)² 1]
= 6250 0.1236 = Rs. 772.5

85. 1460 = P(1 R/100)² …(i)
1606 = P(1 R/100)³ …(ii)
Dividing equation (ii) by (i)
1 R/100 = 1606/1460
R/100 = 1606/1460 146/1460 = 1/10
R = 10%

86. If the distance between the school and home be x km, then
x/3 x/4 = 10/60
x/12 = 1/6
x = 1/6 12 = 2 km

87. 60 kmph = 60 5/18 m/sec
= 50/3 m/sec
If the speed of second train be x m/sec, then
50/3 x = 120/18 = 20/3
x = 50/3 20/3 = 10 m/sec
= 10 18/5 kmph = 36 kmph

89. 8 4m + 6w 8
10 3m + 7 10w

===== Page 16 =====

2m 22w 1m 11w
4m + 6w = 50w
M₁D₁ = M₂D₂
50 8 = 20 D₂
D₂ = 50 8 / 20 = 20 days

90. A + B = 40
B + C = 38
C + A = 42
On adding,
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
= 150000 10/100
= Rs. 15000

92. It is obvious from the pie chart.
Food 23% , Others 20%

93. Housing 15%
Savings 15%

94. Required percentage
= 10 + 12 + 5
= 27%

95. Expenditure on food
= Rs.(150000/100) 23/4
= Rs. 34500

96. Required percentage
= 300/1200 100 = 25

97. Number of persons killed in 2009
= 800 + 200 = 1000

98. It is obvious from the bar diagram.
Required number of the dead = 1200

99. It is obvious from the bar diagram.
Required number of the dead = 150

100. Required average
= 1500/4 1050/4 1300/4 1000/4
= 4850/4 = 1212.5

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