Question

One litre of water is mixed with 3 litres of sugar solution containing 4% of sugar. What is the % of sugar in the solution?
A. 4%
B. 3%
C. 6%
D. None

Answer 1

Hint: we know that 3 litres of sugar solution contain 4% of sugar. Find the volume of sugar in this. Now find the volume of water in this 3 litres of sugar solution by subtracting the total volume with the volume of the sugar in the solution. Now add one litre to the old volume of water and then find the percentage of sugar in the new solution and then evaluate.

Complete step by step solution:
It is given in the question that 3 litres of sugar solution contain 4% of sugar.
To solve this question, first, we find the volume of sugar in the solution before we add one litre of water.
Now we find the volume of sugar in a 3 litre solution.
Since it is 4% of sugar in 3 litre solution,
‘Of’ in the above expression is denoted by the multiplication sign.
It is given by the expression,
$\Rightarrow 3\times \dfrac{4}{100}=0.12$ litres
Now let us find the original amount of water that is already present in the solution.
This is found out by subtracting the volume of sugar from the total volume of the solution.
It is given as,
$\Rightarrow 3-0.12=2.88$ litres.
Now let us add the extra one litre to the old volume of water.
$\Rightarrow 1+2.88=3.88$ litres.
Now as asked in the question, let us find the new percentage of sugar in this solution.
To find this we need to evaluate the ratio of the volume of sugar in solution to the total volume of the solution and then find its percentage.
$\Rightarrow \dfrac{0.12}{3.88}\times 100$
$\Rightarrow 3.092\%$
Hence the new percentage of sugar in the solution is 3.09%.

Note: The symbol of percentage $\%$ denotes that the constant is given out of $100\;$. Whenever percentages are given, we must always convert them into fractions and then solve them to make it easier to simplify. Whenever an answer should be written in percentage form just multiply it with $\dfrac{1}{100}$. The constant in front of the percentage symbol can also be a fraction or a decimal.