Unit 4: Ratio, Proportion, Alligation and Mixture - Practice Quiz

1 What does the ratio compare?

2 What is the simplest form of the ratio ?

3 If and , what is ?

4 Which of the following is a proportion?

5 If 5 pens cost , what is the cost of 1 pen?

6 The present ages of A and B are in the ratio . If A is 10 years old, what is B's age?

7 A father is 40 years old and his son is 10 years old. What is the ratio of their ages?

8 Ravi is 12 years old and his sister is 8 years old. What will be the ratio of their ages after 2 years?

9 The sum of the ages of two friends is 30 years. If their ages are in the ratio , what is the age of the younger friend?

10 A mother is three times as old as her daughter. If the daughter is 10 years old, how old is the mother?

11 In a partnership, profits are generally shared in the ratio of:

12 A and B invest and for the same period. What is their profit-sharing ratio?

13 A invests for one year, while B invests for one year. What is the ratio of their profits?

14 A and B invest equal amounts, but A invests for 12 months and B for 6 months. What is the profit-sharing ratio?

15 A and B share a profit of in the ratio . What is A's share?

16 What is a mixture?

17 Alligation is mainly used to find the:

18 A mixture contains 2 liters of milk and 3 liters of water. What is the total quantity of the mixture?

19 If rice costing per kilogram is mixed with rice costing per kilogram in equal quantities, what is the average cost per kilogram?

20 In a replacement problem, some quantity of a liquid is removed and replaced with:

21 Two numbers are in the ratio . If is added to each number, the ratio becomes . What is the sum of the original numbers?

22 If , , and , what is the value of ?

23 What is the fourth proportional to , , and ?

24 The monthly incomes of A and B are in the ratio , while their monthly expenditures are in the ratio . If each saves per month, what is their total monthly expenditure?

25 The present ages of A and B are in the ratio . Six years ago, their ages were in the ratio . What is the sum of their present ages?

26 A father's present age is three times his son's present age. Ten years ago, the father was five times as old as the son. What is the son's present age?

27 The present ages of A and B are in the ratio . After years, their ages will be in the ratio . What is A's present age?

28 Four years ago, a mother was three times as old as her daughter. Eight years from now, she will be twice as old as her daughter. What is the ratio of their present ages?

29 A invests for months, while B invests for months. If the total profit is , what is B's share?

30 A invests for a year, B invests for months, and C invests for months. If the total profit is , what is B's share?

31 A invests in a business. After months, A withdraws . B invests for the entire year. If the annual profit is , what is A's share?

32 A and B invest capitals in the ratio . A invests for the entire year, while B joins after months. If the annual profit is , what is B's share?

33 Rice costing per kg is mixed with rice costing per kg to obtain a mixture worth per kg. In what ratio should the cheaper rice be mixed with the dearer rice?

34 In what ratio should a salt solution be mixed with a salt solution to obtain a salt solution?

35 A -litre mixture of milk and water is in the ratio . How much water must be added so that the ratio becomes ?

36 Tea costing per kg is mixed with tea costing per kg. The mixture is sold for per kg at a profit of . What is the ratio of cheaper tea to dearer tea?

37 A vessel contains litres of pure milk. Ten litres are removed and replaced with water. This operation is performed twice. How much milk remains after the second replacement?

38 A container holds litres of pure juice. Sixteen litres are removed and replaced with water, and the process is repeated once. How much pure juice remains?

39 A -litre solution contains acid. Ten litres of the solution are removed and replaced with water. What is the new percentage of acid?

40 A vessel contains litres of a milk-water mixture in the ratio . Ten litres of the mixture are removed and replaced with pure milk. What is the final ratio of milk to water?

41 Four positive quantities satisfy , , and . What is ?

42 If , what is ?

43 Positive numbers satisfy , , and . What is ?

44 The incomes of A and B are in the ratio , their expenditures are in the ratio , and their savings are in the ratio . If B saves ₹900 more than A, what is their total income?

45 Eight years ago, the ages of A and B were in the ratio . Twelve years from now, their ages will be in the ratio . What is their present-age ratio?

46 Five years ago, A's age was of B's age. Five years from now, B's age will be of C's age. If their present ages total 76 years, what is the present age difference between C and A?

47 The present ages of A and B are in the ratio . Six years ago, A's age was to C's age as . Six years from now, B's age will be to C's age as . What will be the sum of their ages four years from now?

48 Five years ago, the average age of A, B, and C was 53 years. Their present ages satisfy , and six years from now, . What is the present-age ratio ?

49 A invests ₹60,000 for a year, B invests ₹80,000 after three months, and C invests ₹1,00,000 for the first six months. A receives 10% of the total profit for managing the business; the remaining profit is divided according to capital-time products. If the total profit is ₹34,000, what is A's total share?

50 A and B begin a business with ₹50,000 and ₹60,000. After four months, A withdraws ₹20,000. After six months, B adds ₹30,000. C joins after eight months with ₹90,000. If the annual profit is ₹51,000, what is B's share?

51 A invests ₹80,000 for an entire year. B invests ₹1,20,000 after months and doubles this capital at the end of the ninth month. If their profit-sharing ratio is , after how many months did B join? Assume B joined before the end of the ninth month.

52 A, B, and C start a business with capitals in the ratio . After four months, A doubles the capital, B reduces the capital by half, and C withdraws one-fifth of the capital. If A's annual profit exceeds C's by ₹2,400, what is the total annual profit?

53 A 30% acid solution and a 50% acid solution are mixed. Water equal to one-fourth of the initial mixture's volume is then added, producing a 32% acid solution. In what ratio were the 30% and 50% solutions initially mixed?

54 Two varieties of tea cost ₹240 per kg and ₹300 per kg. During processing, 5% of the mixture's weight is lost. The remaining tea is sold at ₹313.50 per kg, producing an overall gain of 10% on the original mixture's cost. In what ratio were the cheaper and dearer teas mixed?

55 Solutions A and B contain 20% and 50% solute. They are first mixed to form a 32% solution. An 80% solution C is then added so that the final concentration becomes 44%. What is the ratio ?

56 One alloy contains gold and silver in the ratio , while another contains them in the ratio . These alloys are mixed with pure silver to obtain a final mixture containing 45% gold. If pure silver forms one-tenth of the final mixture, what is the ratio of the first alloy, second alloy, and pure silver?

57 A 60-litre vessel contains milk and water in the ratio . First, 15 litres of mixture are removed and replaced with water. Then 12 litres of the new mixture are removed and replaced with milk. What is the final ratio of milk to water?

58 A 100-litre vessel contains a solution that is 80% alcohol. An equal quantity is removed and replaced with water twice. If the final solution is 45% alcohol, how much mixture was removed each time?

59 A vessel initially contains pure milk. One-third of its contents is removed and replaced with water. Next, one-third of the resulting mixture is removed and replaced with milk. Finally, one-third is again removed and replaced with water. What is the final ratio of milk to water?

60 A vessel contains liquids A and B in an unknown ratio. First, 20% of the mixture is removed and replaced with B. Then 25% of the resulting mixture is removed and replaced with A. If the final ratio of A to B is , what was the initial ratio?