A vessel is full of a mixture of spirit and water, in which there is 17% spirit. 10 litres of the solution is drawn and the vessel is filled up with water. The proportion of spirit is now found to be 151/9%. How much does the vessel hold?
Question
A vessel is full of a mixture of spirit and water, in which there is 17% spirit. 10 litres of the solution is drawn and the vessel is filled up with water. The proportion of spirit is now found to be 151/9%. How much does the vessel hold?
Solution
Sure, let's solve this step by step:
Step 1: Let's assume the total volume of the mixture in the vessel is V litres.
Step 2: Initially, the vessel is full of a mixture of spirit and water, in which there is 17% spirit. So, the volume of spirit in the mixture is 17% of V, which is 0.17V litres.
Step 3: 10 litres of the solution is drawn from the vessel. Since the solution is a uniform mixture of spirit and water, the proportion of spirit in the drawn solution is the same as the proportion of spirit in the original mixture. So, the volume of spirit in the drawn solution is 17% of 10 litres, which is 1.7 litres.
Step 4: After drawing the solution, the volume of spirit left in the vessel is 0.17V - 1.7 litres.
Step 5: The vessel is then filled up with water. So, the total volume of the mixture in the vessel remains V litres. The proportion of spirit in the new mixture is 151/9%, which is approximately 16.78%. So, the volume of spirit in the new mixture is 16.78% of V, which is 0.1678V litres.
Step 6: Since the volume of spirit in the vessel doesn't change when water is added, we have the equation 0.17V - 1.7 = 0.1678V.
Step 7: Solving this equation for V gives us V = 1.7 / (0.17 - 0.1678) = 1.7 / 0.0022 = 772.73 litres.
So, the vessel holds approximately 772.73 litres.
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