Question : A mixture of 500 litres of alcohol and water contains 20 percent water. How much more water should be added to this so that the water will become 50 percent in the new mixture?
Option 1: 300 litres
Option 2: 400 litres
Option 3: 350 litres
Option 4: 450 litres
Correct Answer: 300 litres
Solution :
The initial mixture of 500 litres, 20% is water
So, quantity of water = 0.20 × 500 = 100 litres
When we add x litres of water to the mixture,
The total volume of the new mixture becomes (500 + x) litres.
⇒ Quantity of water in new mixture = 0.50 × (500 + x) litres = 100 + x
⇒ 250 + 0.5x = 100 + x
⇒ x = $\frac{150}{0.50}$ = 300
Hence, the correct answer is 300 litres.
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