Two individuals, A and B, rent a field together. A grazes 21 horses for 3 months and 15 cows for 2 months, while B grazes 15 cows for 6 months and 40 sheep for 7.5 months. Given that 3 horses consume the same amount of fodder as 5 cows in one day, and 6 cows consume as much as 10 sheep in one day, what fraction of the rent should A be responsible for?

Explanation

We know that 3 horses eat the same as 5 cows, so 1 horse equals 5/3 cows. Also, 6 cows eat the same as 10 sheep, so 1 cow equals 10/6 = 5/3 sheep. Calculating A's consumption in terms of cows: A grazes 21 horses for 3 months (21*3 = 63 horse-months) and 15 cows for 2 months (15*2 = 30 cow-months). Converting horses to cows: 63 horses-months = 63 * (5/3) = 105 cow-months. Adding cows: 105 + 30 = 135 cow-months. For B: 15 cows for 6 months = 90 cow-months. Converting sheep to cows: 40 sheep for 7.5 months = 300 sheep-months; since 1 cow = 5/3 sheep, 1 sheep = 3/5 cow, so 300 sheep-months = 300 * (3/5) = 180 cow-months. Total for B = 90 + 180 = 270 cow-months. The ratio A:B = 135:270 = 1:2. Therefore, A should pay 1/(1+2) = 1/3 of the rent.