Mathematical Problems (Show your steps/calculation)

Let, x units of 12% acid needs to be mixed with.

According to question

x $\times$ 12% +400 $\times$ 6% = (400+x) $\times$ 10%

$$\begin{gathered} =\frac{12x}{100}+\frac{400\times 6}{100}=\frac{(400+x)\times 10\%}{100} \\ =12x+2400=4000+10x \\ [Multiplying both sides by 100] \\ =2x=1600 \\ \therefore x=\frac{1600}{2}=800 \\ Answer: 800 unites of 12\% acid needs to be mixed. \end{gathered}$$

Let, the price of pen and pencil be x Tk. and y Tk. respectively.

According to question =

2(3x+6y)=12x+4y

=6x+12y=12x+4y

=6x=8y

$\therefore$y=$\frac{6x}{8}=\frac{3x}{4}.............\left(i\right)$

$\therefore$2 pens and 4 pencils cost

=2x+4y

=2x+4$\times \frac{3x}{4}$

=2x+3x

=5x

That means 2x+4y=5x

i.e. the total cost of 2 pens and 4 pencils is equal to the 5 times of one pen.