A company makes a mixture which contains 2% alcohol. If 10 litres of alcohol is added to the mixture, then the concentration increases to 5%. What is the approx. quantity of the mixture?Options 316 315 310 300
Question
A company makes a mixture which contains 2% alcohol. If 10 litres of alcohol is added to the mixture, then the concentration increases to 5%. What is the approx. quantity of the mixture?Options 316 315 310 300
Solution
To solve this problem, we can use the concept of mixtures.
Let's denote the initial quantity of the mixture as 'x' litres.
According to the problem, the initial mixture contains 2% alcohol. So, the quantity of alcohol in the initial mixture is 2/100 * x = 0.02x litres.
Then, 10 litres of alcohol is added to the mixture, increasing the alcohol concentration to 5%. So, the total quantity of alcohol in the new mixture is 0.02x + 10 litres.
The total quantity of the new mixture is x + 10 litres (initial mixture 'x' plus the added 10 litres of alcohol).
The concentration of alcohol in the new mixture is therefore (0.02x + 10) / (x + 10) = 5/100 = 0.05.
We can now solve this equation for 'x':
0.02x + 10 = 0.05(x + 10), 0.02x + 10 = 0.05x + 0.5, 10 - 0.5 = 0.05x - 0.02x, 9.5 = 0.03x, x = 9.5 / 0.03, x = 316.67 litres.
So, the initial quantity of the mixture is approximately 316 litres. Therefore, the closest option is 316.
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