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

  1. $12$
  2. $14$
  3. $13$
  4. $15$
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Given that, the strength of a salt solution is $p \%$ if $100\;\text{ml}$ of the solution contains $p$ grams of salt.

Each of three vessels $A,B,C$ contains $500\;\text{ml}$ of salt solution of strengths $ 10 \%, 22\%$ and $33\%$ respectively. So the initial amount of salt in each vessel.

  • $ A = 500 \times \frac{10}{100} = 50\;\text{ml} $
  • $ B = 500 \times \frac{22}{100} = 110\;\text{ml}$
  • $ C = 500 \times \frac{32}{100} = 160\;\text{ml}$

Now, the $100\;\text{ml}$ of the solution is transferred from vessel $A$ to vessels $B.$

  • Then, salt in vessel $B = 10 \%\;\text{of}\;100 + 110 = \frac{10}{100} \times 100 + 110 = 120$
  • Now, the total salt solution in vessel $B = 500 + 100 = 600\;\text{ml}$
  • So, strength of salt solution in vessel $B = \frac{120}{600}  \times 100\% = 20\%$
  • And, the total salt solution in vessel $A = 500 - 100 = 400\;\text{ml}$

Now, $100\;\text{ml}$ of the solution is transferred from vessel $B$ to vessels $C.$

  • Then, salt in vessel $C = 20 \%\;\text{of}\;100 + 160 = \frac{20}{100} \times 100 + 160 = 180$
  • Now, the total salt solution in vessel $C = 500 + 100 = 600\;\text{ml}$
  • So, strength of salt solution in vessel $C = \frac{180}{600}  \times 100\% = 30\%$
  • And, the total salt solution in vessel $B = 500 - 100 = 400\;\text{ml}$

Now, $100\;\text{ml}$ of the solution is transferred from vessel $C$ to vessels $A.$

  • Then, salt in vessel $A = 30 \%\;\text{of}\;100 + 10\% \;\text{of}\; 400 = 30 + 40 = 70$
  • Now, the total salt solution in vessel $A = 400 + 100 = 500\;\text{ml}$
  • So, strength of salt solution in vessel $A = \frac{70}{500}  \times 100\% = 14\%.$

Correct Answer $:\text B$

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