A farmer sold a calf and a cow for Rs $760$. Find the cost of each. > A farmer sold a calf and a cow for Rs. $760$ Thereby making a profit of $25\%$ on the calf and $10\%$ on the cow. By selling them for Rs. $767.5$ he would have raised a profit of $10\%$ on the calf and $25\%$ on the cow. Find the cost of each. I tried the following: Let the price of a calf be $x$ Let the price of a cow be $y$ $x$$+$$y$$=$Rs$760$ $[\cdots (1)]$ Profit on Rs $x$$=$$x$$/$$4$ Profit on Rs $y$$=$$y$$/$$10$ Therefore, Total profit$=$$5$$x$$+$$2$$y$/$20$ I do not know what to do next.

Let $x$ be the original cost (to the farmer) of a calf.

Let $y$ be the original cost (to the farmer) of a cow.

Then $$x + \frac x4 + y + \frac y{10} = 760 \iff \frac{5x}{4} + \frac{11y}{10} = 760\tag{1}$$

And $$x + \frac x{10} + y + \frac y4 = 767.5\iff \frac{11x}{10} + \frac{5y}{4} = 767.5\tag{2}$$

Now you can solve for $x, y$ to obtain the original cost of a calf and a cow.

If it helps you, multiplying each side of _each_ equation by $20$ will get rid of fractions and decimals: $$25x + 22y = 15200\tag{1}$$ $$22x + 25y = 15350\tag{2}$$