Question : The alcohol and water in a mixture are in the ratio of 4 : 5 respectively. 20-litres water is added to it. If the ratio of alcohol and water in the new mixture is 1 : 3 respectively, then what is the total quantity of the alcohol in the new mixture?
Option 1: $\frac{80}{7}$ liters
Option 2: $15$ liters
Option 3: $\frac{60}{7}$ liters
Option 4: $\frac{90}{11}$ liters
Correct Answer: $\frac{80}{7}$ liters
Solution :
Let the initial quantities of alcohol and water in the mixture as 4$x$ and 5$x$ respectively
The total quantity of the mixture
= 4$x$ + 5$x$ = 9$x$
After adding 20 litres of water, the new quantity of water
= 5$x$ + 20
Now,
⇒ Ratio = $\frac{\text{Quantity of alcohol}}{\text{Quantity of water}}$ = $\frac{1}{3}$
⇒ $\frac{4x}{5x + 20}$ = $\frac{1}{3}$
⇒ 3 × 4$x$ = 1 × (5$x$ + 20)
⇒ 7$x$ = 20
⇒ $x$ = $\frac{20}{7}$
So, total Alcohol in the new mixture = Alcohol in the initial mixture = 4$x$
= 4 × $\frac{20}{7}$ = $\frac{80}{7}$
Hence, the correct answer is $\frac{80}{7}$ litres.
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