A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25%?

Let the volume of the solution with 30 % acid content lie between $$v_1$$ and $$v_2$$, where we get a 20% acid solution for $$v_1$$

For $$v_2$$, we get a 25 % acid solution as the resultant mixture.

=> $$15 \% (200) + 30 \% (v_1) = 20 \% (200 + v_1)$$

=> $$30 + 0.3 v_1 = 40 + 0.2 v_1$$

=> $$0.1 v_1 = 10$$ => $$v_1 = 10 \times 10 = 100$$ litres

Similarly, $$15 \% (200) + 30 \% (v_2) = 25 \% (200 + v_2)$$

=> $$30 + 0.3 v_2 = 50 + 0.25 v_2$$

=> $$0.05 v_2 = 20$$ => $$v_2 = 20 \times 20 = 400$$ litres

$$\therefore$$ For the acid content in the resultant mixture to lie between 20 % and 25 %, the volume of the 30 % concentration acid solution must lie between 100 litres and 400 litres.