Question

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less th an 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Answer 1

Let us consider that x litres of 2% boric acid solution need to be added.

Then, the total mixture is ( x+640 ) litres.

The resulting mixture should be less than 6% but more than 4% .

So, the inequality for x becomes

2% of x+ 8% of 640>4% of ( x+640 ) (1)

2% of x+ 8% of 640<6% of ( x+640 ) (2)

Solve the inequality (i)

2 100 x+ 8 100 ( 640 )> 4 100 ( x+640 ) 2x+5120>4x+2560 5120−2560>4x−2x 2560>2x

Further simplify the above inequality (1)

2560>2x 1280>x x<1280

Solve the inequality (2)

2 100 x+ 8 100 ( 640 )< 6 100 ( x+640 ) 2x+5120<6x+3840 5120−3840<6x−2x 1280<4x

Further simplify the above inequality (2)

1280>4x x>320

Therefore, 320<x<1280 .

Hence, the number of litres of 2% boric acid solution to be added must be more than 320 litres but less than 1280 litres.