Question

In what ratio must 30% and 7.5% stock solutions be combined if preparing a 20% solution?

Answer: [a] as ratio 30%:7.5% (x:y or x to y)

Answer 1

Let x be the quantity of 30% of stock solution

Let y be the quantity of 7.5% stock solution

Both these stock solutions are combined hence we add both these values to give us the final value in x+y in 20% stock solution.

This can be expressed mathematically, considering the value given to us is in percentage form

30%x + 7.5%y = 20%(x+y)

Change percentages into fractions

30/100x + 7.5/100y =20/100(x+y)

Multiplying the equation by 100

30x + 7.5y = 20(x+y)

30x + 7.5y = 20x + 20y

Bringing the x terms and y terms to left and right side of equation respectively

30x -20x = 20y -7.5y

10x= 12.5y

Converting into ratio

X/y=125/10×10

X/y=5/4

Answer: [5:4] as ratio 30%:7.5% (x:y)