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• This paper contains 15 Multiple Choice Questions.
• There is only one correct answer to each question.
Q-1. We have three solutions of milk A, B and C. Solutions A, B and C contain milk and water in the ratios of 1 : 3, 2 : 3 and 3 : 2, respectively. If we mix them in the ratio 1 : 2 : 3, respectively, then what is the ratio of milk and water in the new solution?
Q-2. Two metals X and Y are to be used for making two different alloys. If the ratio by weight of X : Y in the first alloy is 6 : 5 and that in the second is 7 : 13, then how many kilograms of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second, to produce a new alloy containing 40% of metal Y?
Q-3. Gold is 19 times as heavy as water, and copper is 9 times as heavy as water. In what respective ratio should these metals be mixed so that the mixture is 15 times as heavy as water?
Q-4. A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture?
Q-5. There are two alloys of gold, silver and platinum. The first alloy is known to contain 40 percent of platinum and the second alloy is known to contain 26 percent of silver. The percentage of gold is the same in both alloys. Having alloyed 150 kg of the first alloy and 250 kg of the second, we get a new alloy containing 30 percent of gold. How much platinum is there in the new alloy?
Q-6. A flask contains pure milk. Five litres of milk is removed and replaced with water. This process is repeated once more. At this stage, the ratio of water and milk is 15: 49. Find the amount of milk present in the flask at the beginning (in litres). ______
7. A vessel had 20 ml of a mixture of milk and water. The mixture has 40% milk. X ml of milk was added to the mixture. Y ml of water was then added to the mixture. Each of the two additions reverses the ratio of milk and water in the vessel. Find the difference between X and Y. ______
Q-8. Two varieties of coffee — A and B are mixed in the ratio 3: 2. The mixture is sold at Rs.100 per kg at 100% profit. If variety A costs Rs.10 per kg more than variety B, what is the cost of variety B per kg?
Q-9. How many litres of 27% alcohol solution are to be added to 20 litres of 36% alcohol solution to obtain a 30% alcohol solution? ______
Q-10. Alloy X has 75% aluminium and 25% zinc. A certain process decreases the quantity of aluminium by one-fourth and the quantity of zinc by one-eighth. Further applications of the process have the same effect as the first one. The least number of times that the process must be applied to X to obtain an alloy in which the proportion of aluminum is 60% or less is
Q-11. Of the two containers A and B, A contains pure milk and B contains water. 50% of A is shifted to B. After thoroughly mixing it, 50% of the contents in B are shifted to A. Is pure milk to water ratio in A greater than 1? Ι. Initial volume of milk in A ≥ Initial volume of water in B. II. Initial volume of milk in A ≤ Initial volume of water in B.
Q-12. Four gallons are drawn from a case full of wine. It is then filled with water. Four gallons of the mixture are again drawn and the cask is refilled with water. The ratio of the quantity of wine now left in the cask to that of the mixture in it is 36:49. How much does the cask hold?
Q-13. There is a vessel holding 40 L of milk. Four litres of milk is initially taken out from the vessel and 4 L of water is then poured in. After this, 5 L of the mixture is replaced with 5 L of water. And finally, 6 L of the mixture is replaced with 6 L of water. How much milk (in litres) is there in the vessel?
Q-14. From a 3:5 solution of milk and water, 20% is taken out and replaced by milk. How many times should this process be done to make the ratio of milk to water 17:8?
Q-15. Two alloys composed of gold and silver together weigh 20 kg. One lump contains 75% gold and 31.25g /kg silver. Another alloy contains 85% gold and 30g/ kg silver. The total quantity of silver in two lumps is 617.5 g. If the two lumps are melted and formed into one, what percentage of gold will it contain?