Question

To a sugar solution of 3 liters containing 40% sugar, one liter of water is added. The percentage of sugar in the new solution is:
$
  A.13\dfrac{1}{3}\% \\
  B.15\% \\
  C.30\% \\
  D.33\% \\
$

Answer 1

Hint: Here, in the question, we need to first evaluate the volume of the sugar present in 3 liters of the sugar solution. As 1 liter of water has been added to the sugar solution of 30 liters, which makes the total volume of the sugar solution as 4 liters, but the concentration (volume) of the sugar in the sugar solution will remain the same as earlier.

Complete step by step answer:
 The total volume of the sugar solution available is 3 liters, of which 40% is the sugar. So, 40% of 3 liters is the sugar in the sugar solution, which can be calculated as:

$
  {V_s} = 40\% {\text{ of }}3L \\
   = \dfrac{{40}}{{100}} \times 3 \\
   = 1.2L - - - - (i) \\
 $

In the sugar solution, which contains 1.2 liters of sugar, then the volume of water will be:

$
  {V_w} = 3L - 1.2L \\
   = 1.8L - - - - (ii) \\
 $

According to the question, 1 liter of water is added to the sugar solution, so the new volume of the water available in the sugar solution is given as:

$
  {V_w}' = 1.8L + 1L \\
   = 2.8L - - - - (iii) \\
 $

Now, to calculate the volume of sugar in the new sugar solution with $\left( {3L + 1L = 4L} \right)$ of the total sugar solution is given as:

$
  {V_s}' = \dfrac{{{V_s}}}{{{V_t}'}} \\
   = \dfrac{{1.2}}{4} \\
   = 0.3 \\
   = 30\% \\
 $
Hence, the percentage of sugar in the new solution is 30%.
Option C is correct.

Note: It is interesting to note here that even adding 1 liter of water in the sugar solution, the volume (or concentration) of the sugar in the sugar solution will remain the same as earlier as we are adding water, which is just diluting the sugar solution. Moreover, as the quantity of water is increasing in the solution, so the concentration of the sugar (percentage) is decreasing.