# APTITUDE RATIOS PERCENTAGES ALLEGATION MIXTURES PROBLEMS

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RATIOS PERCENTAGE ALLEGATIONS AND MIXTURES

If the price of a commodity increases by X%, then the reduction in the consumption so as not to increase the expenditure
And, in case of a decrease
= X / 100 – X * 100
Let the population of a city be ĹPĺ now and suppose it increases at the rate of R% per annum, then
Population after n- years
= p Î (1 + R/100)n
Population n- years ago
= P / (1 + R/100)n
If A is R% more than B, then B is less than A by
= R / 100 + R * 100
If A is R% less than B, then B is more than A by
= R / 100 – R * 100

Practice Problems

1) In a particular constituency, 60% of voters cast their votes, out of which 4% were rejected. The winning candidate receivedá 75% of the valid votes and bagged a total of 6750 votes. The total no. of voters in the constituency was

2) If the side of a square is increased by 20%, by how much % its area is increased?

3) One side of a square is increased by 10%. To maintain the same area, how much % the other side is to be decreased?

4) Cost of sugar is increased by 20% and consumption is reduced by 10%. What is the net effect on the expenditure?

5) Cost of sugar is decreased by 20%. By how much %, consumption can be increased so as to maintain the same expenditure?

6) A reduction in 20% in the price of sugar enables me to purchase 5 kg more for Rs. 600. What is the price of sugar per kg before reduction of price?

7) The population of a town increased by 10% during the first year and 20% during the second year. If the original population was 5000, what is the present population?

8) The population of a town is increased by 20% during the first year and reduced by 10% during the second year. If the present population is 4320.á What was the population 2 years ago?

9) In measuring the sides of a rectangle, one side is taken 10% in excess and the other side is 20% in deficit. Find the error percent in area calculated from the measurement.

10) An increase of 20% in the price of mangoes enables a person to purchase 4 mangoes less for Rs. 40. The price of 15 mangoes before increase was

11) In an examination, it is required to get 65% of the aggregate marks to pass. A student got 540 marks and failed by 5% of marks. What are the maximum aggregate marks a student can get?

12) A candidate scores 25% and fails by 60 marks, while another candidate scores 50% marks, gets 40 marks more than that of the minimum required marks to pass the examination. The maximum marks for the examination is

13) An employer reduces the number of his employees in the ratio 9 : 8 and increases their wages in the ratio 14 : 15. If the original wage bill was Rs. 18900, the ratio in which the wage bill is decreased, is

14) A bag contains 10-paisa and 25-paisa coins in the ratio 17 : 6. If the total money in the bag is Rs. 112, then find the number of 10-paisa coins.

15) A bag contains Rs. 90 in coins of denominations of 50 paisa, 25 paisa and 10 paisa. If coins of 50 paisa, 25 paisa and 10 paisa are in the ratio of 2 : 3 : 5, then the number of 25 paisa coins in the bag is

16) Two vessels A and B of equal capacities contain mixtures of milk and water in the ratio of 4 : 1 and 3 : 1 respectively. 25% of the mixture from A is taken out and added to B. After mixing it thoroughly, 20% of the mixture is taken out from B and added back to A. The ratio of milk to water in vessel A after the second operation is

17) A student scored 20% marks & failed by 32 marks, while another student who scores 32% marks gets 40 marks more than the minimum required pass marks. What are the maximum marks for the examination?
18) If 2 liter of water is evaporated on boiling from 8 liters of sugar solution containing 5% sugar. Find the % sugar in the remaining solution

19) If Ramĺs income is 40% less than that of Shyamĺs. How much percent Shyamĺs income is more than that of Ramĺs.?

20) A mixture of 90 liters of milk & water contains 20% of water. How much water must be added to the mixture so as to make water content equal to 25%.?

21) The population of a town is 6000. In the next year, if males increase by 8% and females 10%, the population becomes 6530. Find the no. of males in the town

22) An alloy contains copper, zinc& nickel in the ratio of 5: 3: 2. The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5: 2: 3.

23) Two equal vessels are filled with the mixtures of water & milk in the ratio of 3: 4 and 5: 3 respectively. If the mixtures are poured into a third vessel, the ratio of water & milk in the third vessel will be

24) The ratio of the income to expenditure of a family is 10: 7. If the family expenses are 10500/-, then the savings of the family is

25) Veerendhar got 273 marks in an examination and scored 5% more than the pass percent. If Balu got 312 marks, then by what % above the pass marks did he pass the examination.?

26) Due to inflation, there is an increase of 33 1/3 % in the price of bananas. If 3 less bananas are available for 24/-, the present rate of the bananas per dozen is

27) A sample of milk contains 5% water. What quantity of pure milk should be added to 10 liters of milk reduced the water content to 2%

28) In a town, the population was 8000. In one year, male population increased by 10% and female population increased by 8% but the total population increased by 9%. The no. of males in the town was

29) If A exceeds B by 40%, B is less than by C, 20%. Then A: C

30) A mixture contains wine & water in the ratio 3: 2 and another mixture contains them in the ratio 4: 5. How many liters of the latter must be mixed with 3- liters of the former so that the resulting mixture may contain equal quantities of wine & water

31) In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?

33) The price of sugar is reduced by 25% but in spite of the decrease, Ramesh ends up increase his expenditure on sugar by 20%. What is the percentage change in his monthly consumption of sugar

34) A man divides his property so that his sonĺs share to his wifeĺs & wifeĺs share to his daughter both are in the ratio 3:1. If the daughter gets 10000/- less than son, the value of the whole property was

35) To attract more visitors, zoo authority announces 20% discount on every ticket which costs 25 paise. For this reason, sale of ticket increases by 28%. Find the percentage of increase in the no. of visitors ů

36) Between two consecutive years my incomes are in the ratio of 2: 3 and expenses in the ratio 5: 9. If my income in the second year is 45000/- and my expenses in the first year is 25000/-. My total savings for the two years

37) Tea costing 136/- a kilogram is mixed with tea costing 141/- a kilogram in the ratio 2: 3. The cost of one kilogram of the mixture is

38 ) 72% of the students of a certain class took Biology and 44% took mathematics. If each student took at least one of Biology or Mathematics and 40 students took both of these subjects, the total no. of students in the class is

39) Two vessels contain milk and water in the ratio 3: 2 and 7: 3. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ration of milk & water is 2:1 ?

40) A & B earn in the ratio 2: 1. They spend in the ratio 5: 3 and save in the ratio 4: 1. If the total monthly savings of both A & B are 5000/-, the monthly income of B is

41) An employer reduces the no. of his employees in the ratio 9: 8 and increases their wages in the ratio 14: 15. If the original wage bill was 18900/-, find the ratio in which the wage bill id decreased

42) In a laboratory, two bottles contains mixture of acid & water in the ratio 2: 5 in the first bottle and 7: 3 in the second bottle. The ratio in which the contents of these two bottles be mixed such that the new mixer has acid & water in the ratio 2: 3 is

43) A jar contains 10 red marbles & 30 green ones. How many red marbles must be added to the jar so that 60% of the marble will be red

44) In an examination, A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500, the marks obtained by A were

45) The daily wages of worker are increased by 10% but the no. of hours worked by him per week is decreased by 10%. If originally he was getting 2000/- per week, what per week will he get now ?

46) Tea worth 126/- per kg and 135/- per kg is mixed with a third variety in the ratio 1: 1: 2. If the mixture is worth 153/- per kg, the price of the third variety per kg will be

47) A container contains 60 kg of milk. From this container, 6 kg of milk was taken out & replaced by water. This process was repeated further two times. The amount of milk left in the mixture is

48) A water tank contains 5% salt by weight. X- liters of freshwater is added to 40 liters of tank water so that the solution contains 2% salt. The value of X is

49) A vessel is filled with liquid 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup

50) The ratio of the numbers of boys and girls in a school was 5: 3, some new boys & girls were admitted to the school, in the ratio 5: 7. At this, the total no. of students in the school becomes 1200, and the ratio of boys to girls changed to 7: 5. The no. of students in the school before new admissions was

52) The ratio of water & spirit in the mixture is 1: 3. If the volume of the solution is increased by 25% by adding spirit only, what is the resultant ratio of water and spirit ?

53) the ratio of the first & second class fares between Khammam & Vijayawada Railway stations is 4: 1 and that of the no. of passengers traveling by first & second classes is 1: 40. If one day 1100/- are collected as total fare, the amount collected from the first class passenger is

54) In an alloy, the ratio of copper & zinc is 5: 2. If 1.250 kg of zinc is mixed in 17 kg 500 grams of alloy, then the ratio of copper & zinc will be

56) 60 kg of rice-1 at 32/- per kg is mixed with 48 kg of rice-2 and the mixture is sold at the average price of 28/- per kg. If there be no profit or loss due to the sale price, then the price of the second variety of rice is ů

57) A vessel is filled with milk & water. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55% and has 240L mixture. Find the quantity of milk in mixture

58) The height of a tree increases every year 1/4 times. If the present height of the tree is 64 cm, then what will be its height after two years

59) Six liters of a 20% solution of alcohol in water are mixed with 4- liters of a 60% solution of alcohol in water. Find the percentage of alcohol in the mixture

60) here is 1000 liters of milk in a pot. 100 liters of milk is taken out and same amount of water is poured into it. Again 200 liters of mixture is taken out and same amount of water is poured into it and finally 400 liters of mixture is taken out and same amount of water is poured into it, then what is the amount of milk in the resulting mixture

61) In 165 liters of mixtures of milk & water, water is only 28%. The milkman sold 40 liters of this mixture and then he added 30 liters of pure milk and 13 liters of pure water in the remaining mixture. What is the percentage of water in the final mixture ?

62) A solid diamond falls and breaks into three pieces whose weights are in the ratio of 2 : 3 : 4. The value of each piece is directly proportional to the square of their weights. Given that the value of solid diamonds is 24, 300/-, find the loss due to breakage

63) There is a vessel holding 40 litres of milk. 4 litres of milk initially is taken out from the vessel and 5 litres of water is poured in. After this, 6 litres of mixture from this vessel is replaced with 7 litres of water. And finally 8 litres mixture from this vessel is replaced with 9 litres of water. How much of the milk (in litres) is there in the vessel now?

64) Price of an article increases by 26%. A family though increases its expenditure by 10%, can purchase 8 kg less. What amount of article can be purchased at original price?

65) A Jar full of milk contains 40% water. A part of this milk is replaced by another mixture containing 19% water and now the percentage of water is found to be 26%. The quantity of milk replaced is ůůůů.

66) A and B have some Guavas divided between themselves. A says to B ôIf I give you 25% of the Guavas I have, I will still have 2 more Guavas than you have.ö To this, B says ôIf you give me Guavas equal to 70% of what I have now, I will have 4 more Guavas than you have.ö What is the total no. of Guavas that they have

67) Rajni decided to donate 12% of his monthly salary to an orphanage. On the day of donation he changed his mind and donated 2, 400/- which was 125% of what he had decided earlier. How much is Rajniĺs monthly salary ?

68) Harsha has a certain amount of money with him. He can buy either 60 apples or 40 mangoes. He wants to spend only 70% of his money. So he buys 14 mangoes and some apples. Find out the no. of apples purchased by Harsha

69) The wheat sold by a grocer contained 10% low quality wheat. What quantity of good quantityá wheat should be added to 150 kg of wheat so that the percentage of low quality wheat becomes 5%

70) A shopkeeper sells notebooks at the rate of 45/- each and earns a commission of 4%. He also sells pencil box at the rate of 80/- each and earns a commission of 20%. How much amount of commission will he earn in two weeks if he sells 10 notebooks and 6 pencil boxes a day

71) The ratio of milk and water in a mixture of 90 liter is 7 : 2. If some amount of mixture is replaced by water, then the ratio of milk to water becomes 5: 2. Find the quantity of water added to the mixture

72) There is a mixture of alcohol and water of 120 liter. The ratio of alcohol to water is 5 : 3. If a 30% mixture is taken out and the same amount of water is added then find the new ratio of alcohol and water in the mixture

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