Question

A mixture contains alcohol and water in the ratio $4:3$, if $5$ liters of water is added to the mixture, the ratio becomes $4:5$. Find the quantity of alcohol in the given mixture?
A.$5L$
B.$7.5L$
C.$10L$
D.$12L$

Answer 1

Hint: Consider that the mixture is in the ratio of $4x:3x$, now add $5L$ of water to $3x$ and now the resultant is equated to the ratio $4:5$, solve for the value of $x$ and find the quantity of alcohol in the mixture.

Complete step-by-step answer:
Given,
Ratio of alcohol and water in the mixture is $\dfrac{4}{3}$
Ratio of alcohol and water when $5L$ of water additionally added to the mixture is $\dfrac{4}{5}$
So, now by the question the ratio is $\dfrac{{4x}}{{3x}}$
According to the question if $5L$ of water is added to the mixture the ratio becomes $\dfrac{4}{5}$
So,
$
   \Rightarrow \dfrac{{4x}}{{3x + 5}} = \dfrac{4}{5} \\
   \Rightarrow 20x = 12x + 20 \\
   \Rightarrow 8x = 20 \\
   \Rightarrow x = \dfrac{{20}}{8} \\
   \Rightarrow x = \dfrac{5}{2} \\
 $
Initially the quantity of alcohol is $4x$ and the quantity of water is $3x$.
According to the question we need to find the quantity of alcohol in the mixture,
Quantity of alcohol in the mixture=$4x\,L$
Quantity of alcohol in the mixture=$4(\dfrac{5}{2})L$
Quantity of alcohol in the mixture=$10L$
So, option C is correct.

Note: Whenever in mixtures and quantity questions, assume the quantity of the individual solutions of the mixture to be in the form of $\dfrac{{ax}}{{bx}}$, it becomes easy when additionally asked to add or deduct some quantity of solution from the mixture.