90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solutions. Find the amount of each types acids to be mixed to form the mixture.

Problem : 90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solutions. Find the amount of each types acids to be mixed to form the mixture.

Doubt by Muskan

Solution :

Let the amount of acid in 90% pure acid solution be x litres.
and the amount of acid in 97% pure acid solution be y litres.

ATQ

x + y = 21 ---------(1)

Also

90% of x + 97% of y = 95% of 21

(90/100) x + (97/100)y = (95/100)21
90x + 97y = 1995  -------- (2)

Now Multiplying eq (1) via 90

90x + 90 y = 1890
90x + 97y = 1995
-      -             -   
--------------------------
0     -7y = - 105
--------------------------

y = (-105/-7)
y = 105/7
y = 15

putting in equation (1)

x + 15 = 21
x = 21-15
x = 6 

Hence

Amount of acid in 90% pure acid solution is 6 litres
and the amount of acid in 97% pure acid solution is 15 litres.