Question

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

Answer 1

Amount of 12% solution of acid = 600 litres

Let x be the required number litres of 30% acid solution to be added to the given 600 litres of 12% acid solution to make the resulting mixture will be more than 15% but less than 18%.

∴ Total amount of mixture = (600 + x) litres

30% acid solution of x litres + 12% acid solution of 600 litres > 15% acid solution of (600 + x) litres

`30/100 xx x + 12/100 xx 600 > 15/100 xx (600 + x)`

30x + 7200 > 9000 + 15x

30x – 15x > 9000 – 7200

15x > 1800

`x > 1800/5` = 120

x > 120   ......(1)

Also 30% acid solution of x litres + 12% acid solution of 600 litres < 18% acid solution of (600 + x) litres.

`30/100 xx x + 12/100 xx 60  15/100 xx (600 + x)`

30x + 7200 < 18 (600 + x)

30x + 7200 < 10800 + 18x

30x – 18x < 10,800 – 7200

12x < 3600

`x < 3600/12` =300

x < 300  ......(2)

From equations (1) and (2)

We get 120 < x < 300

∴ The numbers of litres of the 30% acid solution to be added is greater than 120 litres and less than 300 litres.