Question

if 40 liters of citrus solution constitutes 48% citric and the remaining portion as sugar solution then how many liters of sugar solution must be added to make it 10% citrus solution

Answer 1

Answer:

hope u understood this if yes then it is my pleasure

Step-by-step explanation:

Given that, 3 litres solution contains 40% sugar

⇒Sugar=

100

40

×3

⇒Sugar=

100

40

×3

⇒Sugar=1.2 l

Percentage of sugar in new solution:

⇒New Sugar=

4

1.2

×100

⇒New Sugar=30%

Answer 2

Given:

if 40 liters of citrus solution constitutes 48% citric and the remaining portion as sugar solution then how many liters of sugar solution must be added to make it 10% citrus solution

Solution:

Understand that, when the solution consist of 48% of citric then the remaining portion as sugar will be 52%.

Now find the amount of sugar initially,

$\[\begin{array}{l}48\% \,{\rm{of}}\,{\rm{citric}} \to 40\,\,{\rm{liters}}\\\therefore 52\% \,{\rm{of}}\,{\rm{sugar}} \to \frac{{40}}{{48}} \times 52\,\,{\rm{liters}}\\ \Rightarrow 52\% \,{\rm{of}}\,{\rm{sugar}} \to \frac{{130}}{3}\,{\rm{liters}}\end{array}\]$

Understand that, to make the citric 10%, only sugar is added to the solution and the quantity of citric remains unchanged.

$\[10\% \,{\rm{of}}\,{\rm{citric}} \to 40\,\,{\rm{liters}}\]$

$\[\therefore 90\% \,{\rm{of}}\,{\rm{sugar}} \to \frac{{40}}{{10}} \times 90\,\,{\rm{liters}}\]$

$\[ \Rightarrow 90\% \,{\rm{of}}\,{\rm{sugar}} \to 360\,{\rm{liters}}\]$

Calculate the quantity of sugar added,

$\[ = 360 - \frac{{130}}{3}\]$

$\[ = \frac{{1080 - 130}}{3}\]$

$\[ = \frac{{950}}{3}\]$

$\[ = 316\frac{2}{3}\,\,{\rm{liters}}\]$

Hence, the  liters of sugar solution must be added to make it 10% citrus solution is $\[316\frac{2}{3}\]$