A farmer sold a cow and an ox for Tk. 80,000 and got a profit of 20% on the cow and 25% on the ox. If he sells the cow and the ox for Tk. 82,000 he gets a profit of 25% on the cow and 20% on the ox. Find the individual cost price of the cow and ox.

প্রশ্নে বলা হচ্ছে, একজন কৃষক একটি গাভী ও একটি ষাঁড় 80,000 টাকায় বিক্রয় করে গাভীতে 20% এবং ষাঁড়ে 25% লাভ করলো । সে যদি গাভী এবং ষাঁড় 8,200 টাকায় বিক্রয় করতো তাহলে সে গাভীতে 25% এবং ষাঁড়ে 20% লাভ করতে পারতো। গাভী ও ষাঁড় প্রত্যেকটির ক্রয়মূল্য কত?

Let, the cost price of Cow be x Tk.

And the cost price of Ox be y Tk.

120%x+125%y = 80,000

$$\begin{gathered} \Rightarrow \frac{120x}{100} + \frac{125y}{100} = 80,000 \\ \Rightarrow 120x+125y = 80,000 \times 100 \\ \therefore 24x+25y = 16,00,000 ........ \left(i\right) [Dividing both sides by 5] \\ Again, 125\%x + 120\%y = 82,000 \\ \Rightarrow \frac{125x}{100} + \frac{120y}{100} = 82,000 \\ \Rightarrow 125x + 120y = 82,000 \times 100 \end{gathered}$$

$$\begin{gathered} \therefore 25x + 24y = 16,40,000 . . . . . . . . \left(ii\right) [Dividing both sides by 5] \\ \left(i\right) \times 25 - \left(ii\right) \times 24 \end{gathered}$$

$$\begin{gathered} \frac{600x+625y = 4,00,00,000 \\ 600x+576y= 3,93,60,000}{\Rightarrow 49y=6,40,000} \\ \therefore y = 13,061.22 \end{gathered}$$

Putting the value of y =13,061.22 in equation (i), we get 

$$\begin{gathered} 24x= 16,00,000-25 \times 13,061.22 \\ \Rightarrow 24x= 16,00,000-3,26,530.61 \\ \Rightarrow 24x= 12,73,469.4 \\ \Rightarrow x = \frac{1273469.4}{24} \\ \therefore x = 53, 061.22 \end{gathered}$$

Answer: The cost of the Cow is Tk. 53,061.22 & The cost of the Ox is Tk. 13,061.22.