Answer
Verified
464.1k+ views
Hint: Assume the required amount of acid to be added be x. Hence form two linear equalities in x. Solve the linear inequations to get the range of values of x. Use the fact that if C and V are the concentration and volume of a solution, respectively, then the amount of solute is equal to CV.
Complete step-by-step answer:
Let the amount of acid to be added be x litres.
Initial concentration of acid = 12%.
Initial volume = 600 litres.
Hence the amount of solute present initially $=600\times \dfrac{12}{100}=72$ units.
Amount of solute added $=\dfrac{30}{100}x=0.3x$ units.
Hence the final amount of solute present in the solution =0.3x
The final volume of the solution = 600+x.
Hence the final concentration of the solution $=\dfrac{72+0.3x}{600+x}\times 100=\dfrac{7200+30x}{600+x}$
Now we have
Final concentration is greater than 15%.
Hence \[\dfrac{7200+30x}{600+x}>15\]
Since x>0, multiplying both sides by 600+x would not change the inequality
7200+30x>9000+15x
Subtracting 15x from both sides, we get
7200+15x>9000
Subtracting 7200 from both sides, we get
15x>1800
Dividing both sides by 15, we get
x>120
Also, we have
Final concentration is less than 18%.
Hence, we have
$\dfrac{7200+30x}{600+x}<18$
Since x>0, multiplying both sides by 600+x would not change the inequality
We have
7200+30x<10800+18x
Subtracting 18x from both sides, we get
7200+12x<10800
Subtracting 7200 from both sides, we get
12x<3600
Dividing both sides by 12, we get
x<300
Hence we have 120Hence the manufacturer must add more than 120 litres but less than 300 litres to the solution.
Note: [1] Here any number between 120 and 300 is the solution of the given problem.
[2] In the question, we have assumed concentration to units of solute per unit volume of solutions.
[3] We have assumed the solute units are additive, i.e. a units +b units = a+b units.
[4] Example of such a concentration is weight/ volume percent.
Complete step-by-step answer:
Let the amount of acid to be added be x litres.
Initial concentration of acid = 12%.
Initial volume = 600 litres.
Hence the amount of solute present initially $=600\times \dfrac{12}{100}=72$ units.
Amount of solute added $=\dfrac{30}{100}x=0.3x$ units.
Hence the final amount of solute present in the solution =0.3x
The final volume of the solution = 600+x.
Hence the final concentration of the solution $=\dfrac{72+0.3x}{600+x}\times 100=\dfrac{7200+30x}{600+x}$
Now we have
Final concentration is greater than 15%.
Hence \[\dfrac{7200+30x}{600+x}>15\]
Since x>0, multiplying both sides by 600+x would not change the inequality
7200+30x>9000+15x
Subtracting 15x from both sides, we get
7200+15x>9000
Subtracting 7200 from both sides, we get
15x>1800
Dividing both sides by 15, we get
x>120
Also, we have
Final concentration is less than 18%.
Hence, we have
$\dfrac{7200+30x}{600+x}<18$
Since x>0, multiplying both sides by 600+x would not change the inequality
We have
7200+30x<10800+18x
Subtracting 18x from both sides, we get
7200+12x<10800
Subtracting 7200 from both sides, we get
12x<3600
Dividing both sides by 12, we get
x<300
Hence we have 120
Note: [1] Here any number between 120 and 300 is the solution of the given problem.
[2] In the question, we have assumed concentration to units of solute per unit volume of solutions.
[3] We have assumed the solute units are additive, i.e. a units +b units = a+b units.
[4] Example of such a concentration is weight/ volume percent.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
A group of fish is known as class 7 english CBSE
The highest dam in India is A Bhakra dam B Tehri dam class 10 social science CBSE
Write all prime numbers between 80 and 100 class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Onam is the main festival of which state A Karnataka class 7 social science CBSE
Who administers the oath of office to the President class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Kolkata port is situated on the banks of river A Ganga class 9 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE