Question

A mixture contains alcohol and water in the ratio of 12 : 5. on adding 14 litres of water, the ratio of alcohol to water becomes 3 : 4. the quantity of alcohol in the mixture is?

Answer 1

$\mathbf{Let \: the \: amount \: of \: alcohol \: is \: \: 12x \: and \: amount \: of \: water \: is \: \: 5x, } \: \:$


$On \: \: adding \: 14 \: litres \: in \: water, ratio \: becomes \: 3 : 4 \\ \\ \\ \\ Hence, \\ \\ \\ \rightarrow \frac{12x}{5x + 14} = \frac{3}{4} \\ \\ \\ \rightarrow 4( 12x ) = 3( 5x + 14 ) \\ \\ \\ \rightarrow 36x = 15x + 42 \\ \\ \rightarrow 36x - 15x = 42 \\ \\ \\ \rightarrow 21x = 42 \\ \\ \rightarrow x = \frac{42}{21} \\ \\ \mathbf{ \rightarrow \: x = 2} \\ \\ \\ \\ \mathbf{ Hence, Amount ( quantity ) \: of \: alcohol = 12x = 12( 2 ) = 24 \: \: litres}$

Answer 2

Answer:

The quantity of alcohol in the mixture is $15\frac{3}{11}$ liters

Step-by-step explanation:

Since, the mixture contains alcohol and water in the ratio of 12 : 5,

Let the alcohol in the mixture = 12x and the water in mixture = 5x,

Where, x is any number,

According to the question,

On adding 14 liters of water, the ratio of alcohol to water becomes 3 : 4.

$\implies \frac{12x}{5x+14}=\frac{3}{4}$

$\implies 48x = 15x + 42$

$\implies 33x = 42$

$\implies x = \frac{42}{33}=\frac{14}{11}$

Thus, the quantity of alcohol in the mixture = 12x

$=12\times \frac{14}{11}=\frac{168}{11}=15\frac{3}{11}\text{ liters}$