A manufacturer has 6000 litres of 12% solution of acid. How many litres of 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% acid ?
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $120 <x< 300$
Let x litre of 30% acid solution be added to 600 litre of 12% acid solution, then
15% of (x + 600) < 30% of x + 12% of 600 < 18% of (x+ 600)
15% of (x + 600) < $\frac{30}{100}x+\frac{12}{100}×600< \frac{18}{100}(x+600)$
$5(x+600)< 10x + 4 ×600 < 6(x+100)$
$5x + 3000 < 10x + 2400 < 6x + 3600$
$3000- 2400 < 10x -5x$ and $ 10x-6x < 3600 - 2400$
$600 < 5x $ and $ 4x < 1200$
$120< x $ and $ x< 300$
$⇒120 < x < 300$
Hence, more than 120 litre but less than 300 litre of 30% acid solution should be added to 600 litre of 12% acid solution.