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Ratio And Proportion

Friday, 26 February 2010 13:25

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( 2 Votes )

Ratio And Proportion

1.    Rs.432 is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share which is equal to 6 times C's share. How much did A get?
A.    Rs.192
B.    Rs.133
C.    Rs.144
D.    Rs.128
Ans : C

2.    If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days?
A.    8 men
B.    12 men
C.    2 men
D.    24 men
Ans : C

3.    Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
A.    48
B.    135
C.    24
D.    None of these
Ans : C

4.    The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is
A.    2:1
B.    5:1
C.    99:61
D.    227:133
Ans : D

5.    A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?
A.    35
B.    30
C.    28
D.    42
Ans : C

6.    A, B and C play cricket. A's runs are to B's runs and B's runs are to C's as 3:2. They get altogether 342 runs. How many runs did A make?
A.    162
B.    108
C.    72
D.    None of these
Ans : A

7.    The monthly salaries of two persons are in the ratio of 4:7. If each receives an increase of Rs.25 in the salary, the ratio is altered to 3: 5. Find their respective salaries.
A.    120 and 210
B.    80 and 140
C.    180 and 300
D.    200 and 350
Ans : D

8.    A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort?
A.    3500
B.    4000
C.    6000
D.    None of these
Ans : B

9.    The ratio of marks obtained by vinod and Basu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted.
A.    150
B.    200
C.    400
D.    None of these.
Ans : B

10.    The present ages of A and B are as 6 : 4. Five years ago their ages were in the ratio 5 : 3. Find their present ages.
A.    42, 28
B.    36, 24
C.    30, 20
D.    25, 15
Ans : C

11.    A, B and C enter into a partnership by investing Rs.3600, Rs.4400 and Rs.2800. A is a working partner and gets a fourth of the profit for his services and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that B gets if A gets a total of Rs. 8000?
A.    4888.88
B.    9333.33
C.    4000
D.    3666.66
Ans : A

12.    A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs.2340, what ill be C's share of the earnings?
A.    Rs.520
B.    Rs.1080
C.    Rs.1170
D.    Rs.630
Ans : A

13.    In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?
A.    1 : 2 : 4
B.    3 : 7 : 6
C.    1 : 4 : 2
D.    None of these
Ans : C

14.    A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg.How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?
A.    1 kg
B.    5 kgs
C.    3 kgs
D.    6 kgs
Ans : B

15.    How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
A.    7 litres
B.    10 litres
C.    5 litres
D.    None of these
Ans : C

16.    How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
A.    20 kgs
B.    12.5 kgs
C.    16 kgs
D.    200 kgs
Ans : A

17.    How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixturecontains milk and water in equal proportion?
A.    4 litres
B.    2 litres
C.    1 litre
D.    1.5 litres
Ans : B

18.    A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?
A.    6 litres
B.    10 litres
C.    30 litres
D.    None of these
Ans : B

19.    A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?
A.    40
B.    30
C.    50
D.    60
Ans : C

20.    From a cask of milk containing 30 litres, 6 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of litres of milk left in the cask?
A.    0.512 liters
B.    12 liters
C.    14.38 liters
D.    15.36 liters
Ans : D

21.    In a km race, A gives B a start of 20 seconds and beats him by 40m. However, when he gives B a start of 25 seconds they finish in a dead heat. What is A's speed in m/sec?
A.    12.5 m/sec
B.    20 m/sec
C.    8 m/sec
D.    10 m/sec
Ans : D

22.    A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec?
A.    8 seconds
B.    10 seconds
C.    16.67 seconds
D.    12.5 seconds
Ans : D

23.    A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey and the predator covers as much distance in 2 leaps as 3 leaps of the prey. Will the predator succeed in getting its food?
A.    Yes
B.    In the 6th leap
C.    Never
D.    Cannot determine
Ans : D

24.    A skating champion moves along the circumference of a circle of radius 21 meters in 44 seconds. How many seconds will it take her to move along the perimeter of a hexagon of side 42 meters?
A.    56
B.    84
C.    64
D.    48
Ans : B

25.    A runs 13/5 times as fast as B. If A gives a start of 240m, how far must the post be so that A and B might reach at the same time.
A.    390 m
B.    330 m
C.    600 m
D.    720 m
Ans : A

26.    A gives B a start of 30 seconds in a km race and still beats him by 20 m. However, when he gives B a start of 35 seconds, they finish the race in a dead heat. How long does A take to run the km?
A.    250 seconds
B.    285 seconds
C.    220 seconds
D.    215 seconds
Ans : D

27.    A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
A.    150
B.    200
C.    100
D.    170
Ans : D

28.    A can give B a start of 50 metres or 10 seconds in a kilometer race. How long does A take to complete the race?
A.    200 seconds
B.    140 seconds
C.    220 seconds
D.    190 seconds
Ans : D

29.    Three runners A, B and C run a race, with runner A finishing 12 meters ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed.
What was the length of the race?
A.    36 meters
B.    48 meters
C.    60 meters
D.    72 meters
Ans : B

30.    P can give Q a start of 20 seconds in a kilometer race. P can give R a start of 200 meters in the same kilometer race. And Q can give R a start of 20 seconds in the same kilometer race. How long does P take to run the kilometer?
A.    200 seconds
B.    240 seconds
C.    160 seconds
D.    140 seconds
Ans : C

1. A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square then its area changes by :

A. 4

B. 144

C. 12

D. 2

E. None of the above.

Ans : A

2. A motorcycle stunts man belonging to a fair, rides over the vertical walls of a circular well at an average speed of 54 kph for 5 minutes. If the radius of the well is 5 meters then the distance traveled is:

A. 2.5 kms

B. 3.5 kms

C. 4.5 kms

D. 5.5 kms

E. None of the above

Ans : C

3. If 1 cm on a map corresponds to an actual distance of 40 kms. And the distance on the map between Bombay and Calcutta is 37.5 cms., the actual distance between them is :

A. 375 kms

B. 3750 kms

C. 1500 kms

D. 1375 kms

E. None of the above

Ans : C

4. A box contains 90 mts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is :

A. 10 kg

B. 10.5 kg

C. 11 kg

D. 11.5 kg

E. None of the above

Ans : D

5. If the radius of a circle is increased by 20% then the area is increased by :

A. 44%

B. 120%

C. 144%

D. 40%

E. None of the above

Ans : A

6. Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $409. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is

A. 120

B. 200

C. 60

D. 24

E. 36

Ans : E

7. A plot of land is in the shape of a trapezium whose dimensions are given in the figure below :

Hence the perimeter of the field is

A. 50 m

B. 64 m

C. 72 m

D. 84 m

E. None of the above

Ans : c

8. Four concentric ( having the same center ) circles with radii, x, 2x, 3x and 4x are drawn to form two rings A and B as shown in the figure.

Ratio of the area of inner ring A to the area of outer ring B is

A. 1 : 2

B. 1 : 4

C. 2 : 3

D. 3 : 7

E. None of the above

Ans : D

9. If 3/p = 6 and 3/q = 15 then p - q = ?

A. 1/3

B. 2/5

C. 3/10

D. 5/6

E. None of the above

Ans : C

10. A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is

A. 36

B. 42

C. 45

D. 48

E. None of the above

Ans : C

11. If the area of two circles are in the ratio 169 : 196 then the ratio of their radii is

A. 10 : 11

B. 11 : 12

C. 12 : 13

D. 13 : 14

E. None of the above

Ans : D

12. A semi-circle is surmounted on the side of a square. The ratio of the area of the semi-circle to the area of the square is

A. 1 : 2

B. 2 : p

C. p : 8

D. 8 : p

E. None of the above

Ans : C

13. Which of the following is the greatest ?

A. 40% of 30

B. 3/5 of 25

C. 6.5% of 200

D. Five more than the square of 3

E. 1/2^-4

Ans : E

14. Two identical taps fill 2/5 of a tank in 20 minutes. When one of the taps goes dry in how many minutes will the remaining one tap fill the rest of the tank ?

A. 5 minutes

B. 10 minutes

C. 15 minutes

D. 20 minutes

E. None of the above

Ans : C

15. If the value of XYZ Company stock drops from $25 per share to $21 per share, what is the percent of the decrease?

A. 4

B. 8

C. 12

D. 16

E. 20

Ans : D

16. If a building b feet high casts a shadow f feet long, then, at the same time of day, a tree t feet high will cast a shadow how many feet long?

A. ft/b

B. fb/t

C. b/ft

D. tb/f

E. t/fb

Ans : A

17. If x, y, and z are consecutive negative integers, and if x > y > z, which of the following must be a positive odd integer?

A. xyz

B. (x - y) (y - z)

C. x - yz

D. x(y + z)

E. x + y + z

Ans : B

18. At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavorsare available?

A. 12

B. 16

C. 20

D. 24

E. 30

Ans : C

19. What is the greatest value of a positive integer n such that 3n is a factor of 1815?

A. 15

B. 18

C. 30

D. 33

E. 45

Ans : C

21. Five years ago, Beth's age was three times that of Amy. Ten years ago, Beth's age was one half that of Chelsea. If C repre- sents Chelsea's current age, which of the following represents Amy's current age?

A. c/6 + 5

B. 2c

C. (c-10)/3

D. 3c-5

E. 5c/3 - 10

Ans : A

22. A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?

A. $160

B. $320

C. $400

D. $720

E. $1,600

Ans : B

23. An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?

A. 4

B. 4.5

C. 5

D. 5.5

E. 6

Ans : E

24. If r = (3p + q)/2 and s = p - q, for which of the following values of p would r2 = s2?

A. 1q/5

B. 10 - 3q/2

C. q - 1

D. 3q

E. 9q/2 - 9

Ans : A

25. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

A. 38

B. 40

C. 44

D. 48

E. 50

Ans : C

26. On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle's diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?

A. (3, 3/2)

B. (1, 2/2)

C. (0, -4)

D. (2/2, 1)

E. (-1, -2/2)

Ans : C

27. If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?

A. 50

B. 100

C. 200

D. 300

E. 400

Ans : D

28. A rectangular tank 10" by 8" by 4" is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?

A. 9

B. 12

C. 16

D. 21

E. 39

Ans : B

29. Point Q lies at the center of the square base (ABCD) of the pyramid pictured above. The pyramid's height (PQ) measures exactly one half the length of each edge of its base, and point E lies exactly halfway between C and D along one edge of the base. What is the ratio of thesurface area of any of the pyramid's four triangular faces to the surface area of the shaded triangle?

A. 3 :√2

B. √5:1

C. 4√3:3

D. 2√2:1

E. 8:√5

Ans : D

31. The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?

A. 6.5

B. 4

C. 3

D. 3.5

Ans : C

32. The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday?

A. 240

B. 210

C. 270

D. 300

Ans : D

33. The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is

A. 24

B. 26

C. 23

D. 22

Ans : A

34. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

A. 57 kgs

B. 56.8 kgs

C. 58.2 kgs

D. 52.2 kgs

Ans : A

35. Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average for all the three classes?

A. 81

B. 81.5

C. 82

D. 84.5

Ans : B

36. The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?

A. 60 kgs

B. 61 kgs

C. 37 kgs

D. None of these

Ans : B

37. The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?

A. 11

B. 12

C. 11.5

D. 12.5

Ans : C

38. The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

A. 13.5

B. 14

C. 15

D. 12.5

Ans : D

39. A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?

A. 8

B. 6

C. 2

D. 4

Ans : C

40. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes.

A. 1044

B. 2088

C. 720

D. 324

Ans : B

41. What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?

A. 2400

B. 2592

C. 2678

D. 2540

Ans : B

42. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

A. 9 years

B. 22 years

C. 18 years

D. 33 years

Ans : B

43. The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

A. 6000

B. 6400

C. 7200

D. 9600

Ans : B

44. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.

A. 5624.32

B. 5630.50

C. 5788.125

D. 5627.20

Ans : A

45. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

A. 9000

B. 6250

C. 8530.80

D. 8780.80

Ans : D

46. Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?

A. Rs.40,000

B. Rs.40,000

C. Rs.12,000

D. Rs.20,000

Ans : B

47. A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?

A. 25 years

B. 40 years

C. 33 years and 4 months

D. Cannot be determined

Ans : A

48. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?

A. 8 years

B. 64 years

C. 72 years

D. 56 years

Ans : D

49. Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.

A. 2088

B. 2000

C. 3087

D. None of these

Ans : C

51. Find the number of triangles in an octagon.

A. 326

B. 120

C. 56

D. Cannot be determined

Ans : C

52. Find the equation of a line whose intercepts are twice of the line 3x - 2y - 12 = 0

A. 3x - 2y = 24

B. 2x - 3y = 12

C. 2x - 3y = 24

D. None of these

Ans : A

53. Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm.

A. 77 sq.cm

B. 38.5 sq.cm

C. 35 sq.cm

D. 70 sq.cm

Ans : B

54. Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).

A. 36

B. 18

C. 15

D. 30

Ans : C

55. A stairway 10ft high is such that each step accounts for half a foot upward and one-foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?

A. 30 ft

B. 33 ft

C. 10 ft

D. 29 ft

Ans : D

56. Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?

A. 6

B. 8

C. 12

D. 3

Ans : C

57. What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?

A. lw/3

B. (2lw)/3

C. (3lw)/4

D. (lw)/2

Ans : D

58. Which of the following is inCorrect?

A. An incentre is a point where the angle bisectors meet.

B. The median of any side of a triangle bisects the side at right angle.

C. The point at which the three altitudes of a triangle meet is the orthocentre

D. The point at which the three perpendicular bisectors meet is the centre of the circumcircle.

Ans : B

59. A and B are two points with the co-ordinates (-2, 0) and (0, 5). What is the length of the diagonal AC if AB form one of the sides of the square ABCD?

A. units

B. units

C. units

D. units

Ans : B

61. If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

A. 10 sides

B. 8 sides

C. 12 sides

D. 9 sides

Ans : A

62. If ABC is a right angle triangle with angle A = 900 and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is Correct?

A. (s - b) (s - c) > s (s - a)

B. (s - a) (s - c) > s (s - b)

C. (s - a) (s - b) < s (s - c)

D. 4s (s - a) (s - b) (s - c) = bc

Ans : C

63. What is the measure of in radius of the triangle whose sides are 24, 7 and 25?

A. 12.5

B. 3

C. 6

D. None of these

Ans : B

64. What is the circum radius of a triangle whose sides are 7, 24 and 25 respectively?

A. 18

B. 12.5

C. 12

D. 14

Ans : B

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