A manufacturer has 640 litres of an 8% solution of boric acid. How many litres of 2% boric and acid solution be added to it so that the boric acid content in the resulting mixture will be more than 4% but less than 6%.

Let x litres of 2% boric and acid solution be added to 640 litres of 8% solution of boric acid.

%Strength =

=

It is given that boric acid content in the resulting mixture ranges from 4% to 6%

Therefore,

Multiplying throughout by 100 in the above equation

4 < < 6

> 4 and < 6

When,

> 4

Multiplying both the sides by (640 + x) in the above equation

> 4(640 + x)

5120 + 2x > 2560 + 4x

Subtracting 2x from both the sides in above equation

5120 + 2x – 2x > 2560 + 4x – 2x

5120 > 2560 + 2x

Subtracting 2560 from both the sides in above equation

5120 – 2560 > 2560 + 2x – 2560

2560 > 2x

Dividing both the sides by 2 in above equation

1280 > x

Now when,

< 6

Multiplying both the sides by (640 + x) in the above equation

< 6(640 + x)

5120 + 2x < 3840 + 6x

Subtracting 2x from both the sides in above equation

5120 + 2x – 2x < 3840 + 6x – 2x

5120 < 3840 + 4x

Subtracting 3840 from both the sides in above equation

5120 – 3840 < 3840 + 4x – 3840

1280 < 4x

Dividing both the sides by 4 in above equation

320 < x

Thus, the value of 2% boric acid solution to be added ranges from:

320 to 1280 litres