A customer bought 5 pencils and 6 erasers at Tk. 80. Next week the price of each pencil increases by 20% . But the price of eases remains unchanged . Now the customer buys 2 pencils and 3 erasers at Tk. 39. Find the new price of each pencil.

Let, the initial price of each pencil is Tk. x

And the initial price of each eraser is Tk y

 According the questions, 5x+6y= 80 …………..(i) 

After price increase of pencil, the new price I pencil is (x+20% of x) Tk.

$x+\frac{20x}{100}=\frac{6x}{5}$ tk. 

According to the question, 

$$\begin{gathered} \left(2\times \frac{6x}{5}\right)+\left(3\times y\right)=39 \\ \Rightarrow \frac{12x}{5}+3y=39 \\ \Rightarrow \frac{12x+15y}{5}=39 \\ \Rightarrow 12x+15y=195 ...........\left(ii\right) \end{gathered}$$ 

Now, multiplying equation (i) by 5 and equation (ii) by 2 and subtracting equation (ii) from equation (i) we get , 

$25x+30y=40024x+30y=390x=10$

New price of a pencil will be = $\frac{6x}{5}=\frac{6\times 10}{5}=12$ tk. 

ans. The new price of each pencil is 12 Tk.