Question

# A 12% brine solution was mixed with a 16% brine solution to produce a 15% brine solution. How much of the 12% brine solution and how much of the 16% brine solution were used to produce 40 L of the 15% solution?

Hint:

### let the 12 % brine solution be x L and the 16% brine solution mixed be y L

Total amount of mixed solution = amount of 12 % solution +amount of 16 % solution

= 40 L

Amount of salt in final brine solution = amount of salt in 15% brine solution

= amount of salt in 12% brine + amount of salt in 16% brine

## The correct answer is: 16%

### Ans :- 30 L of 12% brine solution and 10 L of 16% brine solution

Explanation :-

Step 1:-Frame system of linear equations by given condition

Total amount of mixed solution = amount of 12 % solution +amount of 16 % solution

— Eq1

The amount of salt in 12% of x Litres brine solution =

The amount of salt in 16% of y Litres brine solution =

The amount of salt in 15% of 40 L of brine solution =

Amount of salt in final brine solution = amount of salt in 15% brine solution

= amount of salt in 12% brine + amount of salt in 16% brine

We get, — Eq2

Step 2:- eliminate x to find the value of y .

Doing (Eq2) -3(Eq1) to eliminate x .

∴y = 30

Step 3:- find x by substituting the value of y in eq1.

∴x =10

∴30 L of 12% brine solution and 10 L of 16% brine solution is mixed to get 40 L of 15 % brine solution .

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