Question

John wants to make a $100$ ml of $5\%$ alcohol solution mixing a quantity of a $2\%$ alcohol solution with a $7\%$ alcohol solution. What is the quantity of $2\%$ he should use.

• A. $60$ ml
• B. $80$ ml
• C. $40$ ml
• D. $50$ ml

Answer 1

Answer: (A)

Let $x$ and $y$ be the quantities of the $2\%$ and $7\%$ alcohol solutions to be used to make 100ml of 5%, here we get the equation as,

$\Rightarrow$ $x+y=100$

or $y=100-x$

Now to get the quantity of the solutions we get the equation as,

$\Rightarrow$ $2\%x+7\%y=5\%100$

Now by substituting the value of $y$ in terms of $x$ we get,

$\Rightarrow$ $2\%x+7\%(100-x)=5\%100$

Here by removing the $\%$ sign from both the sides we get,

$\Rightarrow$ $2x+7(100-x)=5\times 100$

$\Rightarrow$ $2x+700-7x=500$

$\Rightarrow$ $-5x=-200$

$\Rightarrow$ $x=40$

as we know $y=100-x$

$\Rightarrow$ $y=100-40$

$\Rightarrow$ $y=60$

$\therefore$ Required answer is $60ml.$