Question

how many litres of 35% sugar solution should be added to a 17% sugar solution to obtain 72 litres of 25 % sugar solution?

Answer 1

Suppose x litres of solution to be added.
So amount of 35% of sugar solution = $x\times \frac{35}{100}=\frac{7x}{20}$
Total amount of solution to be made = 72 litres of 25% = $72\times \frac{25}{100}=18$
And then the amount of 17% of remaining solution = $\left(72-x\right)\times \frac{17}{100}=\frac{17}{100}\left(72-x\right)$
So total amount of the solution is given by;
$$\begin{gathered} \frac{7x}{20}+\frac{17}{100}\left(72-x\right)=18 \\ \Rightarrow \frac{35x+17\left(72-x\right)}{100}=18 \\ \Rightarrow 35x+1224-17x=1800\Rightarrow 18x=1800-1224\Rightarrow 18x=576\Rightarrow x=\frac{576}{18}=32 \end{gathered}$$
Therefore 35% sugar solution needs 32 litres to obtain 72 litres of 25 % sugar solution.