Ten liters of 25 % salt solution and 15 liters of 35 % salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the per cent concentration of salt in the mixture?
Question
Ten liters of 25 % salt solution and 15 liters of 35 % salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the per cent concentration of salt in the mixture?
Solution
Sure, let's solve this step by step:
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First, we need to find out how much salt is in each solution. We do this by multiplying the volume of the solution by the percentage of salt in it.
- For the 10% solution: 30 liters * 10% = 3 liters of salt
- For the 25% solution: 10 liters * 25% = 2.5 liters of salt
- For the 35% solution: 15 liters * 35% = 5.25 liters of salt
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Next, we add up all the salt to find the total amount of salt in the mixture: 3 liters + 2.5 liters + 5.25 liters = 10.75 liters of salt
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We also need to find the total volume of the mixture. We do this by adding up the volumes of all the solutions: 30 liters + 10 liters + 15 liters = 55 liters
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Finally, we find the percentage of salt in the mixture by dividing the total amount of salt by the total volume and multiplying by 100 to get a percentage: (10.75 liters / 55 liters) * 100 = 19.55%
So, the concentration of salt in the mixture is approximately 19.55%.
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