Question

Solve this fast with explanation:A pharmacist needs to strengthen a 15% alcoholic solution to one of 32% alcohol. How much pure alcohol should be added to 800 ml of 15% solution?​

Answer 1

$\huge\text{\underline{Solution:}}$


800 ml of 15% alcohol solution will contain:

$\frac{15}{100} \times 800 = 120$ ml of alcohol

Add x ml of pure alcohol to 800 ml to make it 32% solution.


$\text{\underline{Therefore,}}$

Amount of alcohol = x + 120 ml

Total amount of solution = 800 + x ml


$\text{\underline{Hence,}}$

To get 32% solution,

$( \frac{x + 120}{800 + x} ) \times 100 = 32$

$25x + 3000 = 6400 + 8x$

$17x = 3400$

$x = \frac{3400}{17}$

$x = 200$ ml


$\text{\underline{Therefore,}}$

Add 200 ml of pure alcohol to get 32% solution.

Answer 2

$\mathcal{\huge{\green{\underline{ANSWER}}}}$

As given that

Solution contains 15% alcohol

Volume of solution = 800 ml

Then the volume of pure alcohol present in 800 ml

= $\frac{15}{100} × 800$

= 15 × 8

= 120 ml

Now to make the solution 32% alcohol

let the amount of alcohol to be added be = x ml

Then According to the question

$\frac{ 120 + x }{800 + x } = \frac{32}{100}$

=> (120 +x ) ×100 = 32 × (800 + x)

=> 12000 + 100x = 25600 + 32x

By transferring the variable and constant terms

=> 100x - 32x = 25600 - 12000

=> 68x = 13600

=> x = $\frac{13600}{68}$

=> x = 200

So volume of alcohol which should be added

= $\boxed{\boxed{\boxed{\boxed{200\:ml}}}}$

Hope it helps you