A manufacturer has 800 L of a 10% solution of acid. The range of 35% acid to be added to it is (a, b) such that the acid content in the resultant mixture will be more than 15% but less than 25%, then a + b =

Question

A manufacturer has 800 L of a 10% solution of acid. The range of 35% acid to be added to it is $(a, b)$ such that the acid content in the resultant mixture will be more than 15% but less than 25%, then $a + b =$ ________.

Smart Achievers · Accepted Answer

(1400)

$Let x L of 35 % acid solution is added to the solution.$

$Total mixture = (x + 800) L$

$According to question,$

$35 % of x + 10 % of 800 > 15 % of (x + 800)$

and $35 % of x + 10 % of 800 < 25 % of (x + 800)$

$∴$ $\frac{15}{100} (800 + x) < \frac{35}{100} x + \frac{10}{100} \times 800$

and $\frac{25}{100} (800 + x) > \frac{35}{100} x + \frac{10}{100} \times 800$

$\Rightarrow$ $12000 + 15 x < 35 x + 8000$ and $20000 + 25 x > 35 x + 8000$

$\Rightarrow$ $4000 < 20 x$ and $12000 > 10 x$

$\Rightarrow$ $200 < x$ and $1200 > x$ i.e., $200 < x < 1200$

Thus, $a = 200,$ $b = 1200$

Hence, $a + b = 200 + 1200 = 1400$

Solution

Q.
A manufacturer has 800 L of a 10% solution of acid. The range of 35% acid to be added to it is $(a, b)$ such that the acid content in the resultant mixture will be more than 15% but less than 25%, then $a + b =$ ________.

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Solution

Q. A manufacturer has 800 L of a 10% solution of acid. The range of 35% acid to be added to it is (a, b) such that the acid content in the resultant mixture will be more than 15% but less than 25%, then a+b= ________.

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Q.
A manufacturer has 800 L of a 10% solution of acid. The range of 35% acid to be added to it is $(a, b)$ such that the acid content in the resultant mixture will be more than 15% but less than 25%, then $a + b =$ ________.