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24. 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is | |

A. 20% | B. 33% |

C. 30% | D. 25% |

Answer: Option B

Explanation:

**Solution 1**

We have a 11 litre solution containing 42% of alcohol in the water.

=> Quantity of alcohol in the solution $=\dfrac{11 × 42}{100}$

Now 3 litre of water is added to the solution.

=> Total quantity of the new solution = 11 + 3 = 14

Percentage of alcohol in the new solution $=\dfrac{\dfrac{11 × 42}{100}}{14}× 100$

$=\dfrac{11 × 3}{100} = 33\%$

**Solution 2**

%Concentration of alcohol in pure water = 0

%Concentration of alcohol in mixture = 42

Quantity of water : Quantity of mixture = 3 : 11

Let the %concentration of alcohol in the new mixture $=x$

By rule of alligation,

%Concentration of alcohol in pure water (0) | %Concentration of alcohol in mixture(42) | |||||||||

Mean %concentration $(x)$ | ||||||||||

$42-x$ | $x-0=x$ |

But $(42 - x) : x = 3 : 11$

$\Rightarrow 11(42-x)=3x\\\Rightarrow 42 × 11 - 11x = 3x\\\Rightarrow 14x = 42 × 11 \\\Rightarrow x = 3× 11 = 33$

i.e., Percentage of alcohol in the new mixture is 33%

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