140 liters of a solution is formed by mixing two solutions A and B. The concentrations of milk in A and B are 40% and 7 5%, respectively. If the resultant solution has a milk concentration of 52%, then what is the quantity of A that is there in the resultant solution?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 92 liters
The concentrations of milk in A and B are 40% and 75%, respectively.
Ratio of milk and remaining part in solution A = 40% : (100 - 40)%
= 40% : 60%
=2 : 3
So let's assume the milk and the remaining part in solution A is 2y and 3y.
Ratio of milk and remaining part in solution B = 75% : (100-75) %
= 75% : 25%
= 3:1
So let's assume the milk and the remaining part in solution B is 3z and z.
If the resultant solution has a milk concentration of 52%.
2y + 3z = 140 of 52%
2y + 3z = 72.8 ....Eq.(i)
3y + z = 140 of (100 - 52)%
3y + z = 140 of 48%
3y + z = 67.2
Multiply the above equation by 3.
9y + 3z = 201.6 Eq.(ii)
Eq.(ii) - Eq.(i)
9y + 3z - (2y + 3z) = 201.6 - 72.8
9y + 3z - 2y - 3E = 201.6 - 72.8
7y = 128.8
y = 18.4
Quantity of A in the resultant solution = 2y + 3y
= 5y
= 5 × 18.4
= 92 liters