Question

The quantity of water (in $ml$) needed to reduce $9ml$ shaving lotion containing $50\%$ alcohol to a lotion containing $30\%$ alcohol, is:

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

Given that $9ml$ shaving lotion contains $50\%$ alchohol

$\Rightarrow$Quantity of alchohol$=\frac{50}{100}\times 9$

$\Rightarrow$Quantity of alchohol$=4.5ml$

Let the quantity of water to be added be $xml$

Given that New percentage of alchohol$=30\%$

$\Rightarrow \frac{4.5}{9+x}\times 100=30$

$\Rightarrow \frac{4.5}{9+x}=0.3$

$\Rightarrow 4.5=2.7+0.3x$

$\Rightarrow 0.3x=1.8$

$\Rightarrow x=6$

Thereore, the quantity of water to be added is $6ml$