A mixture contains alcohol and water in the ratio of 4 : 3. If 5 litres of water is added to the mixture the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is = ?

13 litres
24 litres
315 litres
410 litres

Answer:- 1

Explanation:-

Solution:

	Alcohol	:	Water
	4	:	3
Let	4x	:	3x

∴ 5 litres of water is added to the mixture

\begin{aligned} \Rightarrow \frac{4 x}{3 x + 5} = \frac{4}{5} \\ \Rightarrow 20 x = 12 x + 20 \\ \Rightarrow 8 x = 20 \\ \Rightarrow x = \frac{20}{2} \\ \Rightarrow x = \frac{5}{2} \\ Quantity of alcohol \\ \Rightarrow 4 \times \frac{5}{2} = 10 litres \end{aligned}

$\eqalign{ & \Rightarrow \frac{{4x}}{{3x + 5}} = \frac{4}{5} \cr & \Rightarrow 20x = 12x + 20 \cr & \Rightarrow 8x = 20 \cr & \Rightarrow x = \frac{{20}}{2} \cr & \Rightarrow x = \frac{5}{2} \cr & {\text{Quantity of alcohol}} \cr & \Rightarrow {\text{4}} \times \frac{5}{2} = 10\,{\text{litres}} \cr}$