Question

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%.

Answer 1

Let x litre of 3o% acid of solution is required to be added, then Total mixture = (x + 600) litres

We have, 30% of x + 12% of 600 > 15% of (x + 600)

and 30%x + 12% of 600 < 18%(x + 600) or \(\frac{30}{100} x +\frac{12}{100} (600)>\frac{15}{100} (x +600)\)

and \(\frac{30}{100}x + \frac{12}{100} (600)<\frac{18}{100}\) (x + 600) or 30x + 7200 > 15x + 9000

and 30x + 7200 < 18x + 10800 [Multiplying by 100 in both sides] or 30x - 15x > 9000 - 7200

and 30x - 18x < 10800 - 7200 or 15x > 1800 and 12x < 3600 or x > 120

and x < 300

i.e. 120 < x < 300

Thus, the quantity of litres of the 30% solution of acid will have to be more than 120 litres but less than 300 litres.