The strength of a salt solution is $\mathrm{p} \%$ if $100 \mathrm{ml}$ of the solution contains $p$ grams of salt. Each of three vessels $\mathrm{A}, \mathrm{B}, \mathrm{C}$ contains $500 \mathrm{ml}$ of salt solution of strengths $10 \%, 22 \%$ , and $32 \%$ , respectively. Now, $100 \mathrm{ml}$ of the solution in vessel A is transferred to vessel B. Then, $100 \mathrm{ml}$ of the solution in vessel $B$ is transferred to vessel $C$ . Finally, $100 \mathrm{ml}$ of the solution in vessel $C$ is transferred to vessel $A$ . The strength, in percentage, of the resulting solution in vessel $A$ is

$15$

$13$

$14$

$12$

✅ Correct Option: 3

We need to track the salt content and volume changes through each transfer step.

First, let us clarify what "p% strength" means: 100 ml of p% solution contains exactly p grams of salt.

Initial Conditions:

Vessel A: 500 ml of 10% solution → contains $5 \times 10 = 50$ grams of salt

Vessel B: 500 ml of 22% solution → contains $5 \times 22 = 110$ grams of salt

Vessel C: 500 ml of 32% solution → contains $5 \times 32 = 160$ grams of salt

Why multiply by 5? Because 500 ml = 5 × 100 ml, and each 100 ml contains the percentage amount in grams.

Transfer 100 ml from A to B

What moves: 100 ml of 10% solution = 10 grams of salt

After the transfer:

Vessel A: 400 ml with $(50 - 10) = 40$ grams of salt

Vessel B: 600 ml with $(110 + 10) = 120$ grams of salt

New strength of B: $120$ grams in $600$ ml $= 120 \div 6 = 20$ %

Transfer 100 ml from B to C

What moves: 100 ml of 20% solution = 20 grams of salt

After the transfer:

Vessel B: 500 ml with $(120 - 20) = 100$ grams of salt

Vessel C: 600 ml with $(160 + 20) = 180$ grams of salt

New strength of C: $180$ grams in $600$ ml $= 180 \div 6 = 30$ %

Transfer 100 ml from C to A

What moves: 100 ml of 30% solution = 30 grams of salt

After the transfer:

Vessel C: 500 ml with $(180 - 30) = 150$ grams of salt

Vessel A: 500 ml with $(40 + 30) = 70$ grams of salt

Strength of vessel A: $70$ grams in $500$ ml $= 70 \div 5 = 14$ %

The key insight is tracking both the salt content and volume changes at each step, then using the definition that strength = (grams of salt) ÷ (volume in hundreds of ml).

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