Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”.
Question
Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”.
Solution
Let's denote the amount of mixture taken from Vessel A as 'x' litres. Therefore, the amount of mixture taken from Vessel B will be '35 - x' litres (since the total capacity of the new vessel is 35 litres).
The ratio of milk to water in Vessel A is 8:3, which means that 8/11 of the mixture in Vessel A is milk and 3/11 is water.
Similarly, the ratio of milk to water in Vessel B is 5:1, which means that 5/6 of the mixture in Vessel B is milk and 1/6 is water.
The ratio of milk to water in the new 35 litre vessel is 4:1, which means that 4/5 of the mixture in the new vessel is milk and 1/5 is water.
We can set up the following equation based on the amount of milk in the new vessel:
(8/11)x + (5/6)(35 - x) = (4/5) * 35
Solving this equation will give us the value of 'x', which is the amount of mixture that should be taken from Vessel A.
Let's solve it:
Multiply through by 330 to clear the fractions:
240x + 175(35 - x) = 4 * 70 * 35
240x + 6125 - 175x = 9800
65x = 9800 - 6125
65x = 3675
x = 3675 / 65
x = 56.54 litres
But we can't take more than 35 litres from Vessel A (since the new vessel's capacity is only 35 litres). Therefore, there seems to be a mistake in the problem as it's not possible to take 56.54 litres from Vessel A. Please check the problem again.
Similar Questions
Two vessels, A and B, have the same capacity and initially contain milk and water in the ratios of 5 : 1 and 3 : 1, respectively. First, 25% of the mixture from vessel A is removed and poured into vessel B. After thoroughly mixing the contents of vessel B, the same quantity is taken out and added back to vessel A. What is the ratio of milk to water in vessel A after this second transfer?1) 7 : 32) 77 : 233) 49 : 114) 81 : 19
Three vessels whose capacities are in the ratio of 3: 2: 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5: 2, 4: 1 and 4: 1 respectively. Taking 1/3 of first, 1/2 of second and 1/7 of third mixtures, a new mixture kept in new vessel is prepared. The percentage of water in the new mixture is
The milk & water in two vessels A & B are in the ratio 4:3 & 2:3 resp. In what ratio, the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk & half water?Options :7:57:95:93:7
A vessel contains a mixture of milk and water in the respective ratio of 5 : 1. 18 liters of mixture was taken out and replaced with the same quantity of milk so that the resultant ratio between the quantities of milk and water in the mixture becomes 7 : 1 respectively. If 28 liters of the mixture is again taken out from the vessel, what is the quantity (in liters) of water that should be added to make the quantity of milk 70% in the mixture
Three glasses of sizes 3 litres, 4 litres and 5 litres contain mixture of milk and water in the ratio 2: 3, 3: 7 and 4: 11, respectively. The contents of all the three glasses are poured into a single vessel. Find the ratio of milk. Options : 14: 31 15: 21 16: 17 18: 19
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.