How many liters of water must be evaporated from 50 litres of a 3 percent sugar solution to get a 5 percent solution?
Ans choices
(A)2 (B)4 (C)6 (D)10 (E)20
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If the 50-liter solution is 3% sugar, then there are 1.5 litres of sugar in the solution (since 3% of 50 is 1.5)neeg wrote:How many liters of water must be evaporated from 50 litres of a 3 percent sugar solution to get a 5 percent solution?
Ans choices
(A)2 (B)4 (C)6 (D)10 (E)20
Let x be the number of liters that are evaporated.
This means the new volume is 50-x liters, but the amount of sugar remains at 1.5 liters (since no sugar leaves the solution)
We want a 5% solution. In other words 5% of the 50-x liters must be sugar.
In other words 5% of 50-x liters of solution equals 1.5 liters of sugar.
Or . . . (5/100)(50-x) = 1.5 [solve for x]
Multiply both sides by 100 to get: 5(50-x) = 150
Expand: 250 - 5x = 150
Rearrange: 100 = 5x
Solve: 20 = x
Answer: E
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Since only water is evaporating, the amount of sugar does not change.neeg wrote:How many liters of water must be evaporated from 50 litres of a 3 percent sugar solution to get a 5 percent solution?
Ans choices
(A)2 (B)4 (C)6 (D)10 (E)20
Thus, 3% of the original volume must be equal to 5% of the resulting volume:
(.03)(50) = (.05)x
3*50 = 5x
x=30.
Since the total volume decreases from 50 liters to 30 liters, the amount of water removed = 50-30 = 20 liters.
The correct answer is E.
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