A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Find the quantity of each the solutions to get the resultant mixture.

Let x litres be the quantity of the 90% acid solution and y litres be the quantity of the 97% acid solution.

Given,

Total volume = 21 litres

⇒ x + y = 21

⇒ x = 21 - y     ….(1)

Als,

⇒ 90% of x + 97% of y = 95% of 21

⇒ 0.90x + 0.97y = 0.95 × 21

⇒ 0.90x + 0.97y = 19.95     ….(2)

Substituting value of x from equation (1) in (2), we get :

⇒ 0.90(21 - y) + 0.97y = 19.95

⇒ 18.9 - 0.90y + 0.97y = 19.95

⇒ 18.9 + 0.07y = 19.95

⇒ 0.07y = 19.95 - 18.9

⇒ 0.07y = 1.05

⇒ y = $\dfrac{1.05}{0.07} = 15$.

Substituting value of y in equation (1), we get :

⇒ x = 21 - y

⇒ x = 21 - 15

⇒ x = 6.

Hence, 6 litres of 90% acid solution and 15 litres of 97% acid solution are mixed.