Two persons $A$ and $B$ take a field on rent. $A$ put on it 21 horses for 3 months and 15 cows for 2 months; $B$ puts 15 cows for 6 months and 40 sheep for $7\frac{1}{2}$ months. If, in one day, 3 horses eat as much as 5 cows eat and 6 cows as much as 10 sheep, what part of the rent should $A$ pay?
Answer
Answer (as printed):
Explanation
6 cows $\equiv 10$ sheep $\Rightarrow 1$ cow $\equiv \frac{5}{3}$ sheep. 3 horses $\equiv 5$ cows $\Rightarrow 1$ horse $\equiv \frac{5}{3}$ cows $\equiv \left(\frac{5}{3}\times\frac{5}{3}\right)$ sheep $\equiv \frac{25}{9}$ sheep. $\therefore$ Ratio of shares of A and B $=\left[\left(21\times\frac{25}{9}\times3\right)+\left(15\times\frac{5}{3}\times2\right)\right]:\left[\left(15\times\frac{5}{3}\times6\right)+\left(40\times\frac{15}{2}\right)\right]=225:450=1:2$. Hence, part of the rent paid by A $=\frac{1}{3}$.
Explanation as extracted from the printed page; notation may be imperfect.