Question
15 liters are drawn from a cask full of wine and then filled with water. This operation is performed two more times. The ratio of the quantity of wine now left in the cask to that of the water is 8:27. How much wine did the cask hold originally
Solution
Let the quantity of the wine in the cask originally be x liters. Then, quantity of wine left in cask after 3 operations = [x {1 - (15/x)}3] liters Therefore, [x {1 - (15/x)}3Â /x] = 8/27 Â [1 - (15/x)}2] = (2/3)3 x = 45 The original quantity of cask = 45 litersÂ
More Mixture Questions
- A mixture of milk and water contains 40% water. On adding 15 litres of water, the quantity of milk becomes 20% more than that of water. Find the initial qu...
- Two varieties of rice costing Rs 40 per kg and Rs 50 per kg are mixed and sold at Rs 44 per kg without any profit or loss. In what ratio are the two variet...
- A lab technician has a 500-litre solution containing a mix of salt and water in a 9:11 ratio. If 40% of this solution is removed and replaced with an equal...
- An alloy consists of 38% aluminum, 32% copper, and 30% zinc. How much aluminum should be added to 60 kg of the alloy so that the new alloy contains 50% alu...
- A solution contains milk and water in the ratio 4:1. If 25 litres of the 75-litre solution is removed and then 10 litres of water is added, what is the qua...
- A jar contains a mixture of mango juice and water in the ratio of 5:2. 84 litres of the mixture was taken out and 34 litres of water was added to it. If th...
- In a 400 litres mixture of milk and water, the ratio of the milk to water is 4:1. If 20 litres mixture is taken out and replaced by same quantity of water,...
- Mixture ‘E’ of salt and water contains salt and water in ratio 6:5, respectively. What will be the ratio of salt to water in mixture ‘E’ when quantity of s...
- From a container of Beer, a thief has stolen 25 litres of beer and replaced it with same quantity of water. He again repeated the same process. Thus in thr...
- A tea merchant has tea of two kinds, costing Rs 200 per kg and Rs 260 per kg. In what ratio should he mix them so that by selling the mixture at Rs 270 per...
Relevant for Exams:
