Q.A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Mixture Concentration: The Intuition First

Imagine you pour a spoonful of sugar into a glass of water and stir. The sugar disappears, but you know it's still there — the water tastes sweet. How sweet? That's what concentration measures: how much of one thing is mixed into another.

You already understand this intuitively. A "strong" cup of tea has more tea leaves (or a longer steep) than a "weak" one. A salty soup has more salt per spoonful than a bland one. Concentration is just a way to put a number on that feeling of "strong" or "weak."

The Core Idea

Concentration = $\frac{\text{amount of the thing we care about}}{\text{total amount of the mixture}}$

The "thing we care about" is called the solute — it's the substance being dissolved or mixed in. The rest of the mixture is the solvent (or the medium). Together, they form the solution (or mixture).

So for sugar water:

• Solute = sugar
• Solvent = water
• Solution = sugar water

Concentration tells you: out of every spoonful of this mixture, how much is sugar?

The Two Most Common Ways to Express Concentration

1. Mass by Mass (or Weight by Weight) — $\% w/w$

This is the purest, most universal form. It compares masses directly.

Example: If you dissolve 10 g of salt in 90 g of water, the total mass of solution is 100 g. The concentration is:

This means: in every 100 g of this salt water, 10 g is salt. The remaining 90 g is water.

2. Volume by Volume — $\% v/v$

Used when both solute and solvent are liquids (like alcohol in water).

Example: A bottle of whisky labelled "40% alcohol by volume" means: out of every 100 mL of the liquid, 40 mL is pure alcohol.

Why This Matters for Exams

In Indian competitive exams (JEE, NEET, board exams), mixture concentration problems usually fall into two categories:

1. Direct calculation — You're given masses/volumes and asked to find the percentage.
2. Mixing two solutions — You combine two solutions of known concentrations and need the concentration of the final mixture.

For the second type, remember this golden rule: