# Practice Test

Q1) On combining two groups of students having 30 and 40 marks respectively in an exam, the resultant group has an average score of 34. Find the ratio of the number of students in the first group to the number of students in the second group Show Answer

Q2) In what ratio must a grocer mix two varieties of tea costing Rs. 15 and Rs. 20 per kg respectively, so as to get a mixture worth Rs. 16.50 per kg? Show Answer

Q3) How much water must be added to a bucket which contains 40 L of milk at the cost price of Rs. 3.50 per liter, so that the cost of milk reduces to Rs. 2 per liter? Show Answer

Q4) A mixture of certain quantity of milk with 8 L of water is worth 45 paise per liter. If pure milk be worth 54 paise per liter, how much milk is there in the mixture? Show Answer

Q5) A milk seller has a milk of Rs. 100 per liter. In what ratio should water be mixed in that milk, so that after selling the mixture at Rs. 80 per liter, he may get a profit of 50%? Show Answer

Q6) A trader has 50 kg of pulses, part of which he sells at 8% profit and rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit? Show Answer

Q7) 600 g of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution? Show Answer

Q8) A trader has 200 kg of sugar, a part of which he sells at 10% profit and rest at 5% loss. He gains 7% on the whole. What is the quantity sold at 5% loss? Show Answer

Q9) A container is filled with liquid, 6 part of which are water and 10 part milk. How much of the mixture must be drawn off and replaced with water, so that the mixture may be half water and half milk? Show Answer

Q10) 4 L are drawn from a container full of milk and is, then filled with water. This operation is performed three more times. The ratio of the quantity of milk left in the container and that of water is 16 : 65. How much milk did the container hold initially? Show Answer

Q11) Two vessels P and Q contain wine and water in the ratios of 5 : 2 and 8 : 5 respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing wine and water in the ratio of 9 : 4. Show Answer

Q12) In what ratio must a grocer mix rice worth Rs. 30 per kg and Rs. 32.5 per kg, so that by selling the mixture at Rs. 34.10 per kg, he may gain 10%? Show Answer

Q13) A container contains 40 kg of milk. From this container, 4 kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now there in the container? Show Answer

Q14) There are 65 students in a class, Rs. 78 are distributed among them so that each boy gets Rs. 1.6 and each girl gets Rs. 0.60. Find the numbers of boys and girls in the class. Show Answer

Q15) A butler stole wine from a butt of sherry which contained 80% of spirit and he replaced it by wine containing only 32% spirit. Then, the butt was of 48% strength only. How much of the but did he steal? Show Answer

Q16) The total cost price of two watches is Rs. 840 one is sold at a profit of 16% and other at a loss of 2%. There is no loss or gain in the whole transaction. The cost price of the watch on which the shopkeeper gains is Show Answer

Q17) Gold is 19 times and copper is 9 times as heavy as water. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water? Show Answer

Q18) Six liters of a 20% solution of alcohol in water are mixed with 4 liters of a 60% solution of alcohol in water. The % alcoholic strength of the mixture is Show Answer

Q19) A merchant lent out Rs. 1,000 in two parts, one at 8% and the other at 10% interest. The yearly average comes out to be 9.2%. Find the amount lent in two parts. Show Answer

Q20) One liter of water was mixed to 3 liters of sugar. Solution containing 4% of sugar. What is the percentage of sugar in the solution? Show Answer

Q21) How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay? Show Answer

Q22) A trader mixes 80 kg of tea at Rs. 15 per kg with 20 kg of tea at cost price of Rs. 20 per kg. In order to earn a profit of 25%. What should be the sale price of the mixed tea? Show Answer

Q23) A company blends two varieties of tea from two different tea gardens, one variety costing Rs. 20 per kg and other Rs. 25 per kg, in the ratio 5 : 4. He sells the blended tea at Rs. 23 per kg. Find the profit percent Show Answer

Q24) Pure milk costs Rs. 3.60 per liter. A milkman adds water to 25 liters of pure milk and sells the mixture at Rs. 3 per liter. How many liters of water does he add? Show Answer

Q25) In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price? Show Answer

Q26) Two liquids are mixed in the proportion of 3 : 2 and the mixture is sold at Rs. 11 per kg at a 10% profit. If the first liquid costs Rs. 2 more per kg than the second, what does it cost per liter? Show Answer

Q27) A chemist has 10 liters of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many liters of water must he add? Show Answer

Q28) How much water must be added to a cask which contains 40 liters of milk at cost price Rs. 3.5 liters so that the cost of milk reduces to Rs. 2 liter? Show Answer

Q29) The number of milliliters of water added to reduce 9 ml of aftershave lotion, containing 50% alcohol, to a lotion containing 30% alcohol is Show Answer

Q30) In my pocket there are Rs. 25 consisting of only the denominations of 20 paise and 50 paise. Thus there are total 80 coins in my pocket. The no. of coins of the denomination of 50 paise is Show Answer

Q31) There are 65 students in a class. 39 rupees are distributed among them so that each boy gets 80 P and each girl gets 30 P. Find the number of boys and girls in that class. Show Answer

Q32) The ratio of milk and water in 55 liters of adulterated milk is 7 : 4. How much water must be added to make the mixture's ratio 7 : 6? Show Answer

Q33) 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, then the ratio of gold and copper in alloy C will be Show Answer

Q34) A cane contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 liters of mixture are drawn off and the cane is filled with B, the ratio of A and B becomes 7 : 9. How many liters of liquid A was contained by the cane initial. Show Answer

Q35) Five liters of water is added to a certain quantity of pure milk costing Rs. 3 per liter. If by selling mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture? Show Answer

Q36) A jar full of whiskey contains 40% alcohol. A part of this whiskey is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whiskey replaced is Show Answer

Q37) A mixture consists of 15 parts of coffee, purchased at Rs. 2.10 per kg and 1 part of chicory, purchased at 98 paise per kg. If it is sold at Rs. 2.25 per kg, what profit would be made on the sale of 5 quintals? Show Answer

Q38) How many liters of pure alcohol must be added to 10 liters of mixture which is 15% alcohol to make a mixture which will be 25% alcohol? Show Answer

Q39) How many kg of custard powder costing Rs. 40 kg must be mixed with 16 kg of custard powder costing Rs. 55 kg so that 25% may be gained by selling the mixture at Rs. 60 kg? Show Answer

Q40) From a cask full of milk, 10 liters are taken out of 50 liters and is filled with water. This was done twice. What is the quantity of milk now left in the cask? Show Answer

Q41) Two vessels A and B contains spirit and water mixed in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5? Show Answer

Q42) A butter stole wine from a butt of sherry which contained 32% of spirit and then replaced what he stole, by wine containing only 18% spirit. The butt was then of 24% strength only. How much of the butt had he stolen? Show Answer

Q43) Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7, respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together. Show Answer

Q44) Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, then the price of the third variety per kg is Show Answer

Q45) Several liters of acid were drawn off from a 54 liter vessel, full of acid and equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result now, the vessel contained 24 liters of pure acid. How much of the acid was drawn off initially? Show Answer

Q46) An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the tank was half-empty again, it was filled with B type petrol. What is the precentage of A type petrol at present in the tank? Show Answer

Q47) How many kilograms of tea powder costing Rs. 31 per kg be mixed with thirty six kilograms of tea powder costing Rs. 43 per kg, such that the mixture when sold at Rs. 44 per kg gives profit of 10%? Show Answer

Q48) A mixture of Nitric acid and Sulfuric acid is taken in the ratio of 1 : 2 and another mixture of the same is taken in the ratio 2 : 3. How many parts of the two mixtures must be taken to attain a new mixture consisting of Nitric acid and Sulfuric acid in the ratio of 3 : 5? Show Answer

Q49) In two alloys, the ratio of iron and copper is 4 : 3 and 6 : 1, respectively. If 14 kg of the first alloy and 42 kg of the second alloy is mixed together to form a new alloy, then what will be the ratio of iron to copper in the new alloy? Show Answer

Q50) In a mixture of 45 liters, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2? Show Answer

Q51) 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? Show Answer