Question : A 30-litre mixture of milk and water contains 15% water. How much water must be added to it to increase the percentage of water in the solution to 37.5%?
Option 1: 6.0 litres
Option 2: 10.8 litres
Option 3: 7.2 litres
Option 4: 8.4 litres
Correct Answer: 10.8 litres
Solution :
Given,
Total mixture = 30 litres
Water contains = 15% of 30 L = 4.5 litres
Milk contains = (30 – 4.5) L = 25.5 litres
Now we add some water, the water contained in the mixture is 37.5% of the total mixture.
⇒ The ratio of milk and water in the final mixture = 62.5 : 37.5 = 5 : 3
Let us add $x$ litres of water
⇒ $\frac{25.5}{4.5+x}=\frac{5}{3}$
⇒ $76.5 = 22.5 + 5x$
⇒ $5x = 54$
⇒ $x = 10.8$ litres
Hence, the correct answer is 10.8 litres.
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