SSC solved paper of quantitative aptitute 2014
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1. Subhash can copy 50 pages in 10 h; Subhash and Prakash can copy 300 pages in 40 h. In how much time can Prakash copy 30 pages?
(a) 12 h
(b) 9 h
(c) 13 h
(d) 10 h
2. Rajesh is in-charge of buying bread rolls and buns for a party. There are 10 buns in each box of buns and 8 bread rolls in each box of bread rolls. Rajesh wants to buy exactly the same number of buns and bread rolls. What is the smallest number of boxes he should buy for buns alone?
(a) 10
(b) 8
(c) 4
(d) 5
4. If a job is to be completed in 10 days, it requires 270 persons. If 180 persons take up the same job, they will finish it in
(a) 27 days
(b) 12 days
(c) 15 days
(d) 18 days
5. A certain number of men can finish a piece of work in 100 days. However, if there were 10 men less, then it would take 10 days more for the work to be finished How many men were there originally?
(a) 110
(b) 75
(c) 50
(d) 100
6. A square lawn has path 4 m wide around it. If the area of the path is 196 m2, then each side of the lawn is
(a) 7.25 m
(b) 9.25 m
(c) 8.25 m
(d) 8 m
7. A cloth merchant has announced 25% rebate on marked price. If one needs to have a rebate of Rs. 40, then how many shirts, each with a marked price of Rs. 32, should he purchase?
(a) 7
(b) 8
(c) 5
(d) 6
8. One dozen pairs of socks quoted at Rs. 160 are available at a discount of 10%. Find how many pairs of socks can be bought for Rs. 60.
(a) 6 pairs
(b) 8 pairs
(c) 5 pairs
(d) 7 pairs
9. A machine is marked at Rs. 7500 for sale. The shopkeeper allows successive discounts of 8%, 5% and 2% on it. The net selling price (in Rs.) is
(a) 6427.50
(b) 6415.40
(c) 6400.30
(d) 6423.90
10. The surface area of two spheres are in the ratio 4 : 9. What is the ratio of their volumes?
(a) 8 : 27
(b) 16 : 81
(c) 2 : 3
(d) 4 : 9
11. On increasing the diameter of a circle by 75%, the percentage increase in the perimeter is
(a) 75%
(b) 80%
(c) 65%
(d) 70%
12. If the perimeter of an equilateral triangle is 42 cm, its area, (in sq cm) will be
(a) 1
(b) 2
(c) 0
(d) 1/2
(a) –1
(b) 3abc
(c) 1
(d) 0
15. If x + y = 4 and 1/x + 1/y = 4, then the value of x 3 + y 3 is
(a) 52
(b) 64
(c) 4
(d) 25
16. (a 2 + 2a) 2 + 12(a 2 + 2a) – 45 can be expressed as
(a) (a – 1) (a –3) (a2 + 2a + 15)
(b) (a – 1) (a + 3) (a2 + 2a + 15)
(c) (a + 1) (a + 3) (a2 + 2a + 15)
(d) (a + 1) (a – 3) (a2 + 2a + 15)
17. The ratio of the first and second class fares between two stations is 4 : 1 and that of the number of passengers travelling by the first and second class is 1 : 40. If Rs. 11000 is collected as total fare, then the amount collected from the first class passengers is
(a) Rs. 1375
(b) Rs. 3150
(c) Rs. 800
(d) Rs. 1000
18. The average age of three boys is 15 yr. If their ages are in the ratio of 3 : 5 : 7, then the age of the youngest boy (in yr) is
(a) 18
(b) 21
(c) 9
(d) 15
19. Of three numbers, the first is twice the second and the second is thrice the third. If the average of the three numbers is 10, then the largest number is
(a) 12
(b) 18
(c) 30
(d) 15
20. A man purchased a car for Rs. 135000 and spent Rs. 25000 on repairs. At what price was the car sold if he suffered 10% loss on it?
(a) Rs. 176000
(b) Rs. 144000
(c) Rs. 121500
(d) Rs. 150000
21. In the certain examination, 77% candidates passed in English and 34% failed in Mathematics. If 13% failed in both the subjects and 784 candidates passed in both the subjects, then the total number of candidates was
(a) 1600
(b) 1800
(c) 1200
(d) 1400
22. A train 120 m long runs through a station at the speed of 54 km/h. The time taken by the train to pass a man standing on the platform
(a) 7s
(b) 8s
(c) 5s
(d) 6s
23. A, B and C start together from the same point to travel around a circular island 30 km in circumference. A and B are travelling in the same direction and C is in the opposite direction. If A travels 5 km, B travels 7 km and C travels 8 km in an hour, then they all come together again after
(a) 25 h
(b) 30 h
(c) 15 h
(d) 20 h
24. At what rate will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 yr at compound interest?
(a) 6%
(b) 6.5%
(c) 5%
(d) 5.5%
25. Radii of two circles are 6.3 cm and 3.6 cm. If they touch each other internally, then the distance between their centres is
(a) 9.1 cm
(b) 2.7 cm
(c) 3.7 cm
(d) 10.1 cm
26. There is a circle of radius 5 cm and the perpendicular distance from the centre of the circle to the chord of the circle is 3 cm. Then, the length of the chord is
(a) 6 cm
(b) 5 cm
(c) 8 cm
(d) 4 cm
28. The bisector of ÐBAC of DABC cuts BC at and D and the circumcircle of the triangle at E. If DE = 3 cm, AC = 4 cm and AD = 5 cm, then the length of AB is
(a) 9 cm
(b) 10 cm
(c) 7 cm
(d) 8 cm
(a) Side – Angle – Side
(b) Angle – Side – Side
(c) Angle – Side – Angle
(d) Side – Side – Side
30. If an equilateral triangle ABC is inscribed in a circle with centre at 0, then ÐBOC, ÐCOA and ÐAOB are respectively
(a) 50°, 60°, 70°
(b) 120°, 120°, 120°
(c) 60°, 60°, 60°
(d) 80°, 120°, 160°
(a) 198
(b) 234, 216
(c) 216, 234
(d) 198,
32. Given that a + b +c = 2 and ab + bc + ca = 1, then the value of (a + b) 2 + (b + c) 2 + (c + a) 2 is
(a) 10
(b) 16
(c) 6
(d) 8
(a) –1
(b) -1/2
(c) 1
(d) 1/2
34.
35. If in a triangle ABC, AB is smaller than AC, then AC – AB is
(a) = BC
(b) < 1/2 AC
(c) < BC
(d) > BC
38. A kite flying at a height of 45 m from the level ground is attached to string inclined t 60° to the horizontal. The length of the string is
(a) cot A cot B
(b) sec A cosec B
(c) tan A tan B
(d) None of these
41. The angle subtended at the centre of a circle by an arc length equal in length to the radius of the circle is defined as
(a) one radian
(b) 90 degrees
(c) one grade
(d) one degree
42. If sin x + sin 2 x = 1, then the value of cos 2 x + cos 4 x is
(a) 2
(b) 2.5
(c) 1
(d) 1.5
(a) 18°
(b) 14°
(c) 28°
(d) 24°
Directions (Q. Nos. 45-50) Study the following chart and answer the questions given below the chart.
45. If in the year 1998, the boxes were exported at the same rate per box as that in 1997, what would be the value (in crore of Rs.) of export in 1998?
(a) 330
(b) 400
(c) 352
(d) 375
46. What is the difference between boxes (in lakh) exported in the years 1996 and 1997?
(a) 50
(b) 25
(c) 100
(d) None of these
47. In which year was the value per aluminium box the minimum?
(a) 1996
(b) 1998
(c) 1999
(d) 1995
48. What is the difference (in lakh) between the boxes exported in the years 1997 and 1998?
(a) 100000
(b) 1000000
(c) 10
(d) 1000
49. What was the aproximate percentage increase in export value from the years 1995 to 1999?
(a) 375
(b) 200
(c) 333.3
(d) None of these
50. What was the percentage drop in export quantity from the years 1995 to 1996?
(a) 75
(b) 25
(c) 50
(d) None of these
(a) 12 h
(b) 9 h
(c) 13 h
(d) 10 h
2. Rajesh is in-charge of buying bread rolls and buns for a party. There are 10 buns in each box of buns and 8 bread rolls in each box of bread rolls. Rajesh wants to buy exactly the same number of buns and bread rolls. What is the smallest number of boxes he should buy for buns alone?
(a) 10
(b) 8
(c) 4
(d) 5
4. If a job is to be completed in 10 days, it requires 270 persons. If 180 persons take up the same job, they will finish it in
(a) 27 days
(b) 12 days
(c) 15 days
(d) 18 days
5. A certain number of men can finish a piece of work in 100 days. However, if there were 10 men less, then it would take 10 days more for the work to be finished How many men were there originally?
(a) 110
(b) 75
(c) 50
(d) 100
6. A square lawn has path 4 m wide around it. If the area of the path is 196 m2, then each side of the lawn is
(a) 7.25 m
(b) 9.25 m
(c) 8.25 m
(d) 8 m
7. A cloth merchant has announced 25% rebate on marked price. If one needs to have a rebate of Rs. 40, then how many shirts, each with a marked price of Rs. 32, should he purchase?
(a) 7
(b) 8
(c) 5
(d) 6
8. One dozen pairs of socks quoted at Rs. 160 are available at a discount of 10%. Find how many pairs of socks can be bought for Rs. 60.
(a) 6 pairs
(b) 8 pairs
(c) 5 pairs
(d) 7 pairs
9. A machine is marked at Rs. 7500 for sale. The shopkeeper allows successive discounts of 8%, 5% and 2% on it. The net selling price (in Rs.) is
(a) 6427.50
(b) 6415.40
(c) 6400.30
(d) 6423.90
10. The surface area of two spheres are in the ratio 4 : 9. What is the ratio of their volumes?
(a) 8 : 27
(b) 16 : 81
(c) 2 : 3
(d) 4 : 9
11. On increasing the diameter of a circle by 75%, the percentage increase in the perimeter is
(a) 75%
(b) 80%
(c) 65%
(d) 70%
12. If the perimeter of an equilateral triangle is 42 cm, its area, (in sq cm) will be
(a) 1
(b) 2
(c) 0
(d) 1/2
(a) –1
(b) 3abc
(c) 1
(d) 0
15. If x + y = 4 and 1/x + 1/y = 4, then the value of x 3 + y 3 is
(a) 52
(b) 64
(c) 4
(d) 25
16. (a 2 + 2a) 2 + 12(a 2 + 2a) – 45 can be expressed as
(a) (a – 1) (a –3) (a2 + 2a + 15)
(b) (a – 1) (a + 3) (a2 + 2a + 15)
(c) (a + 1) (a + 3) (a2 + 2a + 15)
(d) (a + 1) (a – 3) (a2 + 2a + 15)
17. The ratio of the first and second class fares between two stations is 4 : 1 and that of the number of passengers travelling by the first and second class is 1 : 40. If Rs. 11000 is collected as total fare, then the amount collected from the first class passengers is
(a) Rs. 1375
(b) Rs. 3150
(c) Rs. 800
(d) Rs. 1000
18. The average age of three boys is 15 yr. If their ages are in the ratio of 3 : 5 : 7, then the age of the youngest boy (in yr) is
(a) 18
(b) 21
(c) 9
(d) 15
19. Of three numbers, the first is twice the second and the second is thrice the third. If the average of the three numbers is 10, then the largest number is
(a) 12
(b) 18
(c) 30
(d) 15
20. A man purchased a car for Rs. 135000 and spent Rs. 25000 on repairs. At what price was the car sold if he suffered 10% loss on it?
(a) Rs. 176000
(b) Rs. 144000
(c) Rs. 121500
(d) Rs. 150000
21. In the certain examination, 77% candidates passed in English and 34% failed in Mathematics. If 13% failed in both the subjects and 784 candidates passed in both the subjects, then the total number of candidates was
(a) 1600
(b) 1800
(c) 1200
(d) 1400
22. A train 120 m long runs through a station at the speed of 54 km/h. The time taken by the train to pass a man standing on the platform
(a) 7s
(b) 8s
(c) 5s
(d) 6s
23. A, B and C start together from the same point to travel around a circular island 30 km in circumference. A and B are travelling in the same direction and C is in the opposite direction. If A travels 5 km, B travels 7 km and C travels 8 km in an hour, then they all come together again after
(a) 25 h
(b) 30 h
(c) 15 h
(d) 20 h
24. At what rate will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 yr at compound interest?
(a) 6%
(b) 6.5%
(c) 5%
(d) 5.5%
25. Radii of two circles are 6.3 cm and 3.6 cm. If they touch each other internally, then the distance between their centres is
(a) 9.1 cm
(b) 2.7 cm
(c) 3.7 cm
(d) 10.1 cm
26. There is a circle of radius 5 cm and the perpendicular distance from the centre of the circle to the chord of the circle is 3 cm. Then, the length of the chord is
(a) 6 cm
(b) 5 cm
(c) 8 cm
(d) 4 cm
28. The bisector of ÐBAC of DABC cuts BC at and D and the circumcircle of the triangle at E. If DE = 3 cm, AC = 4 cm and AD = 5 cm, then the length of AB is
(a) 9 cm
(b) 10 cm
(c) 7 cm
(d) 8 cm
(a) Side – Angle – Side
(b) Angle – Side – Side
(c) Angle – Side – Angle
(d) Side – Side – Side
30. If an equilateral triangle ABC is inscribed in a circle with centre at 0, then ÐBOC, ÐCOA and ÐAOB are respectively
(a) 50°, 60°, 70°
(b) 120°, 120°, 120°
(c) 60°, 60°, 60°
(d) 80°, 120°, 160°
(a) 198
(b) 234, 216
(c) 216, 234
(d) 198,
32. Given that a + b +c = 2 and ab + bc + ca = 1, then the value of (a + b) 2 + (b + c) 2 + (c + a) 2 is
(a) 10
(b) 16
(c) 6
(d) 8
(a) –1
(b) -1/2
(c) 1
(d) 1/2
34.
35. If in a triangle ABC, AB is smaller than AC, then AC – AB is
(a) = BC
(b) < 1/2 AC
(c) < BC
(d) > BC
38. A kite flying at a height of 45 m from the level ground is attached to string inclined t 60° to the horizontal. The length of the string is
(a) cot A cot B
(b) sec A cosec B
(c) tan A tan B
(d) None of these
41. The angle subtended at the centre of a circle by an arc length equal in length to the radius of the circle is defined as
(a) one radian
(b) 90 degrees
(c) one grade
(d) one degree
42. If sin x + sin 2 x = 1, then the value of cos 2 x + cos 4 x is
(a) 2
(b) 2.5
(c) 1
(d) 1.5
(a) 18°
(b) 14°
(c) 28°
(d) 24°
Directions (Q. Nos. 45-50) Study the following chart and answer the questions given below the chart.
45. If in the year 1998, the boxes were exported at the same rate per box as that in 1997, what would be the value (in crore of Rs.) of export in 1998?
(a) 330
(b) 400
(c) 352
(d) 375
46. What is the difference between boxes (in lakh) exported in the years 1996 and 1997?
(a) 50
(b) 25
(c) 100
(d) None of these
47. In which year was the value per aluminium box the minimum?
(a) 1996
(b) 1998
(c) 1999
(d) 1995
48. What is the difference (in lakh) between the boxes exported in the years 1997 and 1998?
(a) 100000
(b) 1000000
(c) 10
(d) 1000
49. What was the aproximate percentage increase in export value from the years 1995 to 1999?
(a) 375
(b) 200
(c) 333.3
(d) None of these
50. What was the percentage drop in export quantity from the years 1995 to 1996?
(a) 75
(b) 25
(c) 50
(d) None of these
Answer Key
1. (a) 2. (c) 3. (a) 4. (c) 5. (a) 6. (c) 7. (c) 8. (c) 9. (d) 10. (a)
11. (a) 12. (b) 13. (d) 14. (d) 15. (a) 16. (b) 17. (d) 18. (c) 19. (b) 20. (b)
21. (d) 22. (b) 23. (b) 24. (c) 25. (b) 26. (c) 27. (a) 28. (b) 29. (b) 30. (c)
31. (d) 32. (c) 33. (a) 34. (d) 35. (c) 36. (a) 37. (d) 38. (c) 39. (b) 40. (c)
41. (a) 42. (c) 43. (b) 44. (c) 45. (c) 46. (d) 47. (d) 48. (c) 49. (c) 50. (b)
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