A) More than \[250\text{ }L\]and less than \[~300\]
B) More than \[300\text{ }L\] and less than \[400\]
C) More than \[100\text{ }L\] and less than \[250\]
D) More than \[250\text{ }L\]and less than \[350\]
Correct Answer: C
Solution :
Let x litre of 40% acid solution is required to be added. Then, Total mixture \[=(x+500)L\] \[\therefore \] \[40%\] of \[x+10%\] of \[500>15%\] of \[(x+500)\] \[\Rightarrow \] \[\frac{40x}{100}+\frac{10\times 500}{100}>\frac{15}{100}\times (x+500)\] \[\Rightarrow \] \[40x+5000>15x+7500\] \[\Rightarrow \] \[25x>2500\] \[\Rightarrow \] \[x>100\] ?..(i) Also, \[40%\] of \[x+10%\] of \[500<20%\] of \[(x+500)\] \[\Rightarrow \] \[\frac{40}{100}x+\frac{10}{100}\times 500<\frac{20}{100}(x+500)\] \[\Rightarrow \] \[40x+5000<20x+10000\] \[\Rightarrow \] \[20x<5000\] \[\Rightarrow \] \[x<250\] ?..(ii) From Eqs. (i) and (ii), we get required range, is more than \[100L\]and less than \[250L\].
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