A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%.

Let x litres of 30% acid solution be added to 600 litres of 12% acid solution. Then,

Total quantity of mixture = (600 + x) litres

Total acid content in the (600 + x) litres of mixture must be more than 15% and less than 18%. Therefore,

⇒ 15% of (600 + x) < (30x / 100 + 12 × 600 / 100) < 18% of (600 + x)

⇒ (15 / 100)(600 + x) < (30x / 100 + 12 × 600 / 100) < (18 / 100)(600 + x)

⇒ 15(600 + x) < 30x + 12 × 600 < 18(600 + x)     [Multiplying throughout by 100]

⇒ 9000 + 15x < 30x + 7200 < 10800 + 18x

⇒ 9000 + 15x < 30x + 7200 and 30x + 7200 < 10800 + 18x

⇒ 9000 − 7200 < 30x − 15x and 30x − 18x < 10800 − 7200

⇒ 1800 < 15x and 12x < 3600

⇒ x > 120 and x < 300

Hence, 120 < x < 300.