The total price of Cricket bat and ball is 1,350. If the price of bat increases 25% and the price of ball decreases 20% then the total price of bat and ball remains same. Find the prices of bat and ball?

প্রশ্নে বলা হচ্ছে, একটি ব্যাট ও বলের দাম 1,350 টাকা। ব্যাটের দাম 25% বাড়লে এবং বলের দাম 20% কমলেও ব্যাট-বলের মোট দাম 1,350 টাকাই থাকে। ব্যাট ও বলের দাম কত?

Let, the price of a bat is x Tk. & The price of a ball is y Tk.

According to question, x + y = 1,350 . . . . . . . . . . . . (i)

Now, increased price of a bat = x + x of 25% $= x + \frac{25x}{100} = \left(x + \frac{x}{4}\right) = \frac{5x}{4}Tk.$

$$\begin{gathered} And decreased of a ball = y - y of 20\% = y - \frac{20y}{100} = \left(y - \frac{y}{5}\right) = \frac{4y}{5} Tk. \\ According to question,\frac{5x}{4} + \frac{4y}{5} = 1,350 \\ \Rightarrow \frac{25x + 16y}{20} = 1,350 \\ \therefore 25x+16y=27,000 . . . . . . . . .\left(ii\right) \\ Multiplying equation \left(i\right) by 25 \& Subtracting equation \left(ii\right) from equation \left(i\right) \\ \frac{25x + 25y = 37,750 \\ 25x + 16y =27,000}{9y = 6,750} \\ \therefore y = \frac{6750}{9} =750 \\ And, x = 1,350-750 = 600 \\ So, price of bat is 600 Tk. \& Price of ball is 750 Tk. \left(ans\right) \end{gathered}$$