A farmer sold a cow and an ox for Rs. 800 and got a profit of 20% on the cow and 25% on the ox. If he sells the cow and the ox for Rs. 820 he gets a profit of 25% on the cow and 20% on the ox. The individual cost price of the cow and the ox is :

Answer: Option A

Let the C.P. of the cow be Rs. x and that of the ox be Rs. y
Then,
= 120% of x + 125% of y = 800
$$\Rightarrow \frac{6x}{5}+\frac{5y}{4}=800$$
⇒ 24x + 25y = 16000 .......(i)
And
125% of x + 120% of y = 820
$$\Rightarrow \frac{5x}{4}+\frac{6y}{5}=820$$
⇒ 25x + 24y = 16400 ......(ii)
Adding (i) and (ii), we get :
49x + 49y = 32400
$$\Rightarrow x+y=\frac{32400}{49}......(iii)$$
Substracting (i) from (ii), we get :
x - y = 400 ........(iv)
Adding (iii) and (iv), we get :
$$\begin{array}{rl}& 2x=\frac{32400}{49}+400\\ & =\frac{52000}{49}\\ & \Rightarrow x=\frac{26000}{49}\approx 530.60\\ & \text{Putting }x=\frac{26000}{49}\text{ in }(iii),\\ & \text{we get}:\\ & y=\frac{32400}{49}-\frac{26000}{49}\\ & =\frac{6400}{49}\approx 130.60\end{array}$$