book Maths Puzzle Numerical Ability

A chemist mixes a 10% acid solution with a 50% acid solution to form 400ml. of a 40% solution. How much of each solution should be used in the mixture.

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book Other Question

The difference between two numbers is -38. Two times the smaller number minus five times the larger number is -217. What are the two numbers? How can I simplify this equation to easily find the solutions for x and y to this equation:

x*y = (x+y)*(x+y-1)/4

Thanks