logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities
0 votes

How many liters of water will have to be added to $1125$ liters of the $45\%$ solution of acid so that the resulting mixture will contain more than $25 \%$ but less than $30\%$ acid content ?

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
  • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
  • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
Let x be the liters of water added to 1125 liters of 45 % acid solution
total mixture $= (x+1125)$
The amount of acid content in the mixture is $45 \% \;of\;1125$
The resulting mixture will contain more than $25 \%$ acid content.
Hence $25\%$ of $(1125 +x) < 45 \%$ of $1125$
$=> \large\frac{25}{100} $$(1125 +x) < \large\frac{45}{100 } $$\times 1125$
Multiplying both sides by 100
$=> 25 (1125 +x) < 45 \times 1125$
$=> 25 x +25 \times 1125 < 45 \times 1125$
Subtracting $25 \times 1125$ on both sides.
=> $ 25 x < 45 \times 1125 -25 \times 1125$
=> $ 25 x < (45- 25) \times 1125$
=> $25 x < 20 \times 1125$
dividing by 25 on both sides
=> $ x < \large\frac{20 \times 1125}{25}$
=> $ x < 900$
The resulting solution must be less than $30 \%$ acid content.
$45 \%$ of $1125 < 30 \%$ of (1125+x)
$\large\frac{45}{100} $$ \times 1125 < \large\frac{30}{100} $$(1125 +x)$
Multiplying both sides by 100.
$45 \times 1125 - 30 \times 1125 < 30x$
Subtracting both sides by $30 \times 1125$
=> $ 45 \times 1125 -30 \times 1125 < 30 x$
=> $15 \times 1125 < 30x$
Dividing by 30 on both sides
$\large\frac{1125 \times 15}{30 } $$ < x$
$562.5 < x $------(2)
We see from (1) and (2) that x must be more than $562.5 \;litres$ and less than 900 litres
The solution set is $ 562.5 < x< 900$
answered Aug 5, 2014 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...