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 :

Solution(By Examveda Team)

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 :
$$\eqalign{ & 2x = \frac{{32400}}{{49}} + 400 \cr & \,\,\,\,\,\,\,\,\, = \frac{{52000}}{{49}} \cr & \Rightarrow x = \frac{{26000}}{{49}} \approx 530.60 \cr & {\text{Putting }}x = \frac{{26000}}{{49}}{\text{ in }}(iii), \cr & {\text{we get}}: \cr & y = \frac{{32400}}{{49}} - \frac{{26000}}{{49}} \cr & \,\,\,\,\,\, = \frac{{6400}}{{49}} \approx 130.60 \cr} $$