Multiple choice

$90 \%$ acid solution $(90 \% $pure acid and $10 \ $ water) and$ 97 \%$ acid solution are mixed to obtain $21 $ litres of $95\%$ acid solution. How many litres of each solution are mixed?

  1. $2$  litres and  $14$  litres
  2. $8$  litres and $35$  litres
  3. $7$  litres and $25$  litres
  4. $6$  litres and $15$  litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x litres of 90% and (21 - x) litres of 97% be mixed. Then 0.90x + 0.97(21 - x) = 0.95*21, giving x = 6 litres of 90% solution and 15 litres of 97% solution.

AI explanation

Using the rule of alligation on the percentage concentrations, we write 90 and 97 on the left, and 95 in the middle. Taking the differences of the diagonals gives a ratio of (97 minus 95) to (95 minus 90), which is 2 to 5 for the 90 percent and 97 percent solutions respectively. Since the total mixture is 21 litres, the quantities are (2 divided by 7) times 21 litres and (5 divided by 7) times 21 litres, resulting in 6 litres of the 90 percent solution and 15 litres of the 97 percent solution.

Keep practicing — related questions