ration proportion

8/13/2019 Ration Proportion

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INFANT JESUS GROUP OF ENGINEERING COLLEGES

PLACEMENT TRAINING QUANTITATIVE APTITUDE

RATIO AND PROPORTION

a : b represents the fractionba

.

The multiplication or division of each term of a ratio by a nonzero number does not affect theratio.

The equality of two ratios is called proportion.

It is written as a: b = c: d or a: b:: c : d. Here, the first and fourth terms are called extremes whilethe second and third terms are called means.

In a proportion, product of extremes = product of means. i.e. ad = bc.

Ifd c

ba

thend cd c

baba

d d c

bba

d d c

bba

,,

PROBLEMS

1.

The ratio55.3

2:4 is the same asa) 4 : 1 b) 2 : 1 c) 7 : 5 d) 7 : 10

Answer: a) 4 : 1

Solution: 55.3 2:4 = 2 7 : 2 5 = 2 2 : 1

2. Two whole numbers whose sum is 64 cannot be in the ratio:a) 5 : 3 b) 7 : 1 c) 3 : 4 d) 9 : 7

Answer: c) 3 : 4

Solution: 3 + 4 does not divide 64.

In all the other cases, the sum divides 64


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6. A bag contains 50 paise, 25 paise and 10 paise coins in the ratio 5: 9: 4 amounting to Rs.206. Thenumber of 25 paise coins isa) 200 b) 360 c) 160 d) 260

Answer: b) 360Solution: The number of 25 paise coins must be a multiple of 9.

The only multiple of 9 in the given answers is 360

7. If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14 then the value of c isa) 7 b) 2 c) 6 d) 8

Answer: c) 6Solution: Let a + b=6k

a+b = 6k; b + c =7k, c + a =8k;

Adding, 2 (a + b + c) = 21 k

k =

=

c = (a + b + c) (a + b) = 14 (6 x ) = 6

8. An amount of Rs.2430 is divided among A, B, C such that if their shares be reduced by Rs.5,Rs.10 and Rs.15 respectively, the remainders shall be in the ratio 3: 4: 5. The share of B isa) Rs.605 b) Rs.790 c) Rs.800 d) Rs.810

Answer: d) Rs.810Solution: Amount after reducing = 2430-(5+10+15)= 2400

Ratio of shares 3 : 4 : 5 => 12 k = 2400; k = 200

Share of B= 4 k + 10 = 810

9. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of thesecond to the third is 5 : 8 then the second number isa) 20 b) 30 c) 48 d) 58

Answer : b) 30

Solution: F : S : T2 : 3

5 : 8

10 : 15 : 24

49 k = 98; k = 2; 15K = 30


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10. If three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862, the middlenumber will bea) 7 b) 14 c) 21 d) 35

Answer: b) 14Solution: (9 + 4 + 25 )k 2=1862 , if the numbers are 3k, 2k , 5k

38k 2 = 1862; k 2 = 49; k = 7; 2k =14

11. In a school 10% of the boys are same in number as 1/4 th of the girls and 10% of the girls are samein number as 1/25 th of the boys. What is the ratio of boys to girls in that school?a) 3 : 2 b) 5 : 2 c) 2 : 1 d) 4 : 3

Answer: b) 5: 2Solution: 10% of the boys = ( )B= ; =

= We dont need the other conditionat all.

12. The incomes of A, B, C are in the ratio of 7: 9: 12 and their spending are in the ratio of 8: 9: 15.If A saves 1/4 th of his income, then the savings of A, B, C are in the ratio ofa) 56: 99: 69 b) 99: 56: 69 c) 69: 56: 99 d) 99: 69: 56Answer: a) 56: 99: 69

Solution: Incomes be 7x, 9x,12xSpending be 8y,9y,15y

Savings will be 7x -8y, 9x 9y, 12x- 15y

The middle part has to be a multiple of 9,This is the only option.

13. Ramana divides two sums of money among his four sons Ganesh, Mahesh, Anil and Sunil. Thefirst sum is divided in the ratio 4: 3: 2: 1 and second in the ratio 5: 6: 7: 8. If the second sum istwice the first, the largest total is received bya) Ganesh b) Mahesh c) Anil d) Sunil

Answer: a) Ganesh

Solution: Let the first sum be 4x, 3x, 2x, xSecond sum be 5y, 6y, 7y, 8yThe second sum is twice the first sum26y = 20x; 13y = 10xTake y=10 x= 13G:M:A:S4X+5Y: 3X+6Y: 2X +7Y: X+8Y102: 99: 96: 93


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14. 20 litres of a mixture contains milk and water in the ratio 5: 3. If 4 litres of this mixture arereplaced by 4 litres of milk, the ratio of milk to water in the new mixture will becomea) 2 : 1 b) 7 : 3 c) 8 : 3 d) 4 : 3

Answer: b)7: 3

Solution: M: W5: 3After 4 litres of mixture removed also the ratio remains the same.The contents will be 10litres milk and 6litres water.After 4 litres of milk added, the ratio is 14: 6 = 7: 3

15. Aand B are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7: 11respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of goldand copper in C will bea) 5 : 9 b) 5 : 7 c) 7 : 5 d) 9 : 5Answer: c) 7: 5

Solution: 9kg of A contains 7G, 2C18Kg of B contains 7G, 11CTake 18kg of A and 18kg of BWe get 21G, 15C7: 5

16. A mixture contains milk and water in the ratio 5: 1. On adding 5 litres of water, the ratio of milkto water becomes 5: 2. The quantity of milk in the original mixture is :a) 16 litres b) 25 litres c) 22.75 litres d) 32.5 litres

Answer: b) 25 litres

Solution: M: W5k: k5litres of water is added.5k : k+5 =5 : 210k = 5k +25; k =5The quantity of milk in the original mixture= 5k= 25

17. Two equal glasses are respectively31

and41

full of milk. They are then filled with water and the

contents mixed in a tumbler. The ratio of milk and water in the tumbler is :a) 7 : 5 b) 7 : 17 c) 9 : 21 d) 11 : 23

Answer: b) 7: 17Solution: m : w

+ +

4+3 : 8+9 (multiplying by 12)7:17


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18. If A : B = 3 : 4 and B : C = 8 : 9 then A : C is equal toa) 1 : 3 b) 3 : 1 c) 2 : 3 d) 3 : 2

Answer c) 2 : 3

Solution: A : B :C3 :4

\ 8 :96 : 8 : 9TAKING lcm for B ratios and multiplying the ratios suitablyA : C IS 6 :9 , 2:3

19. If A : B = 5 : 7 and B : C = 6 : 11 then A : B : C isa) 55: 77: 66 b) 30: 42: 77 c) 35: 49: 42 d) none of these

Answer: b) 30: 42: 77Solution: A : B : C

5 : 76 :1130 : 42 : 77TAKING lcm for B ratios and multiplying the ratios suitably

20. Two numbers are in the ratio 3: 5. If each number is increased by 10, the ratio becomes 5: 7. Thenumbers area) 3, 5 b) 7, 9 c) 13, 22 d) 15, 25

Answer: d) 15, 25Solution: Let the numbers be 3k, 5k

After increasing by 10,

3k + 10 : 5k +10 = 5 :74k =20, k=5The numbers are 15, 25

21. The speeds of three cars are in the ratio 3: 4: 5. The ratio between times taken by them to travelthe same distance isa) 3: 4: 5 b) 5: 4: 3 c) 12: 15: 20 d) 20: 15: 12

Answer:d) 20: 15: 12

Solution: Ratio of speeds is 3 : 4 : 5

Ratio of times is 1/3 :1/4 : 1/520: 15:12 multiplying by the lcm 60

22. 94 is divided into two parts in such a way that fifth part of the first and eighth part of the secondare in the ratio 3 : 4. The first part isa) 27 b) 30 c) 36 d) 48

Answer: b) 30


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Solution: F/5: S/8 = 3: 44F / 5 = 3S /832 F =15SF: S = 15:3230:64 to make the sum 94

23. Divide Rs.171 into two parts whose ratio will be 9:10.a) 56, 115 b) 81, 90 c) 63, 108 d) 108, 63

Answer: b) 81, 90

Solution: 19k = 171K=9The amounts will be 9k, 10k81,90

24. Find the ratio of 2.5 litre to 750ml.a) 3 : 10 b) 3 : 4 c) 10 : 3 d) 12 : 13

Answer:c) 10 : 3

Solution: ratio of 2.5 litre to 750ml is 2500/ 750 =10/3

25. If 2A = 3B = 4C, then A : B : C isa) 2: 3: 4 b) 4 : 3 : 2 c) 6 : 4 : 3 d) 3 : 4 : 6

Answer: c) 6 : 4: 3

Solution:A/B = 3/2 , B/C =4/3A :B :C3 :24 :36 : 4 :3TAKING lcm for B ratios and multiplying the ratios suitably

26. If743cba

thenc

cba is equal to

a) 7 b) 2 c) 21

d) 71

Answer: b) 2Solution: =

= =

= ; =


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27. Five bananas and four apples cost as much as 3 bananas and 7 apples. The ratio of the cost of one banana to that of one apple isa) 3 : 2 b) 4 : 3 c) 3 : 4 d) 1 : 3

Answer:a) 3: 2

Solution: 5B + 4A =3B+ 7A2B = 3A; =

28. The ratio of income of A to that of B is 5: 4 and the expenditure of A to that of B is 3: 2. If at theend of the year, each saves Rs.800, the income of A isa) Rs.1600 b) Rs.1800 c) Rs.2000 d) Rs.2200

Answer: c) Rs.2000Solution: Income - expenditure for A is 5x 3y

Income - expenditure for B is 4x 2y5x 3y = 800; 4x 2y = 800Subtracting x y =0; x = y2x =800; x =400; 5x =2000

29. Rs.53 is divided among A, B, C such that As share is Rs.7 more than Bs share and Bs share isRs.8 more than Cs share. The ratio of their shares isa) 16: 9: 18 b) 25: 18: 10 c) 18: 25: 10 d) 15: 8: 30

Answer: b) 25: 18: 10Solution: A = B +7, B = C+8

A + B + C =53(B+7) +B+ (B-8) =53B = 18

A:B:C = 25 :18:10

30. 85 Kg of a mixture contains milk and water in the ratio 27: 7. How much more water is to beadded to get a mixture containing milk and water in the ratio 3 : 1.a) 5Kg b) 6.5Kg c) 7.25Kg d) 8 KgAnswer: a) 5Kg

Solution: M :W27 :7

67 : 17 Multiplying by 2 to make the sum 8567 : 17 + x adding x kg of water

67 : 17 + x = 3:167 = 52 + 3x; x = 5


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31. Two numbers are in the ratio of 3: 5. If 9 be subtracted from each, they are in the ratio of 12: 23.The first number isa) 27 b) 33 c) 55 d) 49 e) none of these

Answer:b) 33Solution: 3x -9 : 5x -9 = 12 :23

69x- [9 x 23] = 60x [ 9 x 12]9x = 99; 3x=11; 3x = 33

32. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 3 : 7 then A : B : C : D isa) 2 : 4 : 3 : 7 b) 2 : 12 : 15 : 7 c) 8 : 12 : 15 : 35d) 8 : 12 : 16 : 35

Answer: c) 8 : 12 : 15 : 35Solution: A:B:C:D

2:34:58:12:15

3:78 : 12 : 15 : 35

33. Two numbers are such that their difference, their sum and their product are in the ratio 1: 7: 24.The product of the numbers isa) 6 b) 12 c) 24 d) 48Answer: d) 48

Solution: a-b :a+b :ab1: 7 : 24

(a+b) 2 (a-b) 2 = 4ab; (7k) 2 k 2 = 4 24kk=2; 24k =48

35. The ratio of number of males to number of females in a club is 7: 4. If there are 84 males in theclub, the total number of members in the club isa) 126 b) 132 c) 136 d) 148

Answer: b) 132Solution: M : F

7 : 4

84 : 48,multiplying by 12The total number is 84+48

36. A map is drawn on the scale of 4mm for each 16Km. Two places are shown on the map at adistance of 7.2mm. How far away they are from each other?a) 22.3Km b) 9.21Km c) 28.8Km d) 21.8Km

Answer: c) 28.8Km


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Solution: 4mm => 16km7.2 mm => x 7.2 = 28.8 km

37. The ratio of two numbers is 3: 8 and their difference is 115. The greater number isa) 69 b) 184 c) 230 d) 240

Answer:b) 184Solution: S : G

3: 83k , 8k and the difference is 5k5k = 115, k=23The greater number is 8k= 184

38. If32

ba

and54

cb

thencbba

is

a) 5 : 9 b) 8 : 15 c) 20 : 27 d) 27 : 20

Answer:c) 20 : 27Solution: = => =

= ; = =>

= =

multiplying = =

39. If 3x = 8y and 5y = 9z then z x

is

a) 1572

b) 1583

c) 89

d) 8311

Answer: a)1572

Solution: = , =

Multiplying, = =

40. The marks obtained by Suresh in English, Maths and Science are in the ratio 53

:31

:21

. If his

total score is 860, his marks in English isa) 160 b) 228 c) 312 d) 300

Answer: d) 300Solution: E : M : S

1/2 ; 1/3 : 3/5


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15 : 10 : 18, multiplying by 3043 k = 860; k= 20

Marks in English = 15k = 300

41. Solve 2x + 1 : x + 5 = 6x 7 : 3x + 5a) 8 b) 4 c) 6 d) 2

Answer:b) 4Solution: (2x + 1) (3x + 5 ) = ( x + 5 ) ( 6x -7 )

In both sides we get 6x 2

Hence 13x + 5 = 23x 3510x = 40; x = 4

42. What number should be subtracted from both the terms of the ratio 15:19 to make it as 3: 4?a) 3 b) 5 c) 6 d) 9

Answer: a)3Solution: 15-x: 19 x = 3:4

60- 4x = 57 3x; x = 3

43. The average age of three boys is 25 years and their ages are in the ratio 3: 5: 7. The age of theyoungest boy isa) 21 years b) 18 years c) 15 years d) 9 years

Answer:c) 15 years

Solution: average age = 25Sum of their ages = 75

15k= 75; k=5Age of the youngest boy = 3k = 15

44. X, Y and Z share a sum of money in the ratio 7: 8: 16. If z receives Rs.27 more than X then thetotal money shared wasa) Rs.48 b) Rs.93 c) Rs.279 d) Rs.558

Answer: b) Rs.93

Solution: Z receives 27 more than x16k 7k = 279k = 27; k =3

Total money = (7+8+16)k = 93

45. Rs.1870 is divided into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. The third part isa) Rs.510 b) Rs.680 c) Rs.850 d) Rs.1020


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Answer:d) Rs.1020Solution: F/2 = S/3= T/6

T = 2S = 3FF + S + T = 1870T( 1/3 +1/2 + 1 ) = 1870T= 1870 x = 170 x 6 = 1020

Or the third part is a multiple of 6 and is large

46. A 24 litres mixture contains water and milk in the ratio 3: 5. How much water should be added tothis mixture to reverse this ratio?a) 10 b) 12 c) 15 d) 16

Answer:d) 16Solution: W : M

3: 59 :15 to make the sum 249 + x : 15 = 5 : 327 + 3x = 75; x = 16

47. The diameters of the fore wheel and the rear wheel of a tractor are in the ratio 1: 4. When thefore wheel makes 100 revolutions per minute, how many revolutions per minute would the rearwheel make?a) 18 b) 23 c) 25 d) 17

Answer: c) 25Solution: ratio of diameters1 : 4

Ratio of circumferences 1: 4Ratio of revolution 1 :1/44: 1

100 : 25

48. A business man prints two types of prices on his goods; one is for cash payment and other forthose who pay after one month. If the rate of interest is 12% then the two prices are in the ratio

a)101100

b)100101

c)5150

d)5051

Answer: a) 101

100

Solution: Rate of interest 12 % means interest for Rs100 for 1 year is 12 RsInterest for Rs.100 for 1 month is Re1The ratio is 100 : 101


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49. If 512:216: 33 ba thenbaba

is

a) 6 b) 7 c) -7 d) -6

Answer: c) -7

Solution: a 3/ b 3 = = 6 3 / 8 3

a/b = 6/8 , = = ( ) = -7

50. In a factory men, women and children were employed in the ratio 8:5:1to finish a job and theirindividual wages were in the ratio 5:2:3. Total daily wages of all amount to Rs.318. Find the totaldaily wages paid to each category.a)Rs.240,60,18 b)Rs.210,70,38 c)Rs.190,95,33 d)none of these

Answer:a) Rs.240,60,18

Solution: M : W : C8 : 5 : 1

Individual wages 5 : 2 : 3Category wages 8x5 : 5x2 : 1x3

40 : 10 : 353k = 318g

Total daily wages paid to each category Rs.240,60,18

ration proportion

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