Jackie has two solutions that are $2$ percent sulphuric acid and $12$ percent sulphuric acid by volume respectively. If these solutions are mixed in appropriate quantities to produce $60$ litres of a solution that is $5$ percent sulphuric acid, approximately how many litres of the $2$ percent solution will be required?

Using the method of alligation for the 2 percent and 12 percent solutions to achieve a 5 percent mixture, the ratio of their quantities is (12 minus 5) to (5 minus 2), which simplifies to 7 to 3. This means the 2 percent solution makes up 7 parts out of the total 10 parts of the final mixture. Since the final mixture is 60 liters, the required volume of the 2 percent solution is 7/10 of 60, which equals 42 liters. The required volume is 42 liters.

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