1. If a : b = 5 : 9 and b : c = 4: 7, find a : b : c. ans: 20:36:63

2. If x : y = 3 : 4, find (4x + 5y) : (5x – 2y). ans: 32/7

3. Divide Rs. 672 in the ratio 5 : 3. Ans: 420, 252

4. Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20. Ans: 490, 392, 280

5. A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type. Ans: 200, 360, 160

6. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture?(10 litres)

**EXERCISE**

1. If A : B = 3 : 4 and B : C = 8 : 9, then A : C is :

2. If A : B = ½ : 3/8 B : C = 1/3 : 5/9 C:D = 5/6 : ¾ then the ratio A : B: C: D is :

3. If A : B = 5 : 7 and B : C = 6 : 11, then A : B : C is :

4. If A : B : C = 2 : 3 : 4, then A/B:B/C:C/A is equal to :

5. If A : B = 8 : 15, B : C = 5 : 8 and C : D = 4 : 5, then A : D is equal to :

6. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, then A : B : C : D is :

7. If 2A = 3B = 4C, then A : B : C is :

8. If 2A = 3B and 4B = 5C, then A : C is :

9. If A/3 = B/4 = C/5, then A : B : C is :

10. The ratio of 4

^{3.5}: 2^{5}is same as :11. If 0.75 : x : : 5 : 8, then x is equal to :

12. If 1/5 : 1/x = 1/x : 1/1.25, then then the value of x is :

13. If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is :

14. If 15% of x = 20% of , then x : y is :

15. If (x : y) = 2 : 1, then (x

^{2}– y^{2}) : (x^{2}+ y^{2}) is :16. If 5x

^{2}– 13xy + 6y^{2}= 0, then x : y is :17. If (4x

^{2}– 3y^{2}) : (2x^{2}+ 5y^{2}) = 12 : 19, then (x : y) is :18. If x

^{2}+ 4y^{2}.= 4xy, then x : y is :19. If x/5 = y/8 then (x + 5) : (y + 8) is equal to :

20. If a/3 = b/4 = c/7 , then (a+b+c)/c is equal to :

21. If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and (a + b + c) = 14, then the value of c is :

22. If Rs. 782 be divided into three parts, proportional to ½ : 2/3 : ¾ , then the first part is :

23. The salaries of A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

24. If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is :

25. Two numbers are in the ratio 1 : 2. If 7 is added to both, their ratio changes to 3 : 5. The greatest number is:

26. Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

27. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there are Rs. 30 in all, how many 5 p coins are there?

28. Rs.1210 were divided among A, B, C so tnat A : B = 5 : 4 and B : C = 9 : 10. Then, C gets:

29. The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is:

30. The ratio of three numbers is 3 : 4 : 7 and their product is 18144. The numbers are:

31. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s present salary?

32. If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets ¼ of what C gets, then their shares are respectively :

33. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is :

34. Rs. 366 are divided amongst A, B and C so that A may get ½ as much as B and C together, B may get 2/3 as much as A and C together, then the share of A is :

35. A fraction which bears the same ratio to 1/27 that 3/11 does to 5/9 is equal to :

36. A sum of Rs. 1300 is divided amongst P, Q, R and S such that = = = Then, P’s share is :

37. A and B together have Rs. 1210. If 4/15 of A’s amount is equal to 2/5 of B’s amount, how much amount does B have?

38. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

39. Two whole numbers whose sum is 72 cannot be in the ratio :

40. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

41. If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

42. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will, be the new ratio?

43. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?

44. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

45. In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is :

46. Ratio of the earnings of A and B is 4 : 7. If the earnings of A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8 : 7.What are A’s earnings?

47. What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders may be proportional?

48. The fourth proportional to 5, 8, 15 is :

49. The mean proportional between 234 and 104 is :

50. The third proportional to 0.36 and 0.48 is :

51. The ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is

52. In a ratio, which is equal to 3 : 4, if the antecedent is 12, then the consequent is :

53. The third proportional to (x

^{2}– y^{2}) and (x – y) is :54. The prices of a scooter and a TV. are in the ratio 7 : 5. If the scooter costs Rs. 8000 more than a TV. set, then the price of a TV set is :

55. An amount of Rs. 2430 is divided among A, B and C such that if their shares be reduced by Rs. 5, Rs. 10 and Rs. 15 respectively, the remainders shall be in the ratio of 3 : 4 : 5. Then, B’s share was:

56. An amount of Rs. 735 was divided between A, B and C. If each of them had received Rs. 25 less, their shares would have been in the ratio of 1 : 3 : 2. The money received by C was:

57. An alloy is to contain copper and zinc in the ratio 9 : 4. The zinc required to be melted: with 24 kg of copper is:

58. The ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is:

59. 60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, then the amount of tin in the new alloy is:

60. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

61. 15 litres of mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed with it, the percentage of alcohol in the new mixture would be:

62. 20 litres of a mixture contains milk and water in the ratio 5 : 3. If 4 litres of this mixture be replaced by 4 litres of milk, the ratio of milk to water in the new mixture would be:

63. 85 kg of a mixture contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1?

64. The ages of A and B are in the ratio 3 : 1. Fifteen years hence, the ratio will be 2 : 1. Their present ages are:

65. The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is:

66. The speeds of three cars are in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel the same distance is:

67. In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is:

68. The sides of a triangle are in the ratio ½ : 1/3 : ¼ and its perimeter is 104 cm. The length of the longest side is:

69. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the students does not get the scholarship?

70. In a school, 10% of the boys are same in number as 1/4

^{th}of the girls. What is the ratio of boys to girls in that school?71. Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water jn the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and wafer in the fourth container is:

72. x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to:

73. The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Rs 1800. In another month 620 units are consumed and the1 bill is Rs. 2040. In yet another month 500 units are consumed. The bill for that month would be:

74. If 10% of x – 20% of y, then x: y is equal to :

75. Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?

76. The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs. 1600, then the income of A is:

77. The compounded ratio of (2 : 3), (6 : 11) and (11 : 2) is :

78. If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :

79. The least whole number which when subtracted from both the terms of the ratio 6 : 7 gives a ratio less than 16 : 21 is :

80. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be:

81. A certain amount was divided between A and B in the ratio 4 : 3. If B’s share was Rs. 4800, the total amount was:

82. Which of the following ratios is greatest?

83. A sum of Rs. 53 is divided among A, B, C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is:

84. What is the ratio whose terms differ by 40 and the measure of which is 2/7?