Two farmers, X and Y, hire a field. X keeps 18 oxen there for 5 months and 20 goats for 3 months. Y keeps 24 goats for 7 months and 30 sheep for 6 months. If 2 oxen eat as much as 5 goats, and 3 goats eat as much as 4 sheep, what fraction of the total rent should X pay?

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Accepted Answer

1. Convert to goat units: from 2 oxen = 5 goats we get $1	ext{ ox}=2.5	ext{ goats}$. From 3 goats = 4 sheep we get $1	ext{ sheep}=0.75	ext{ goats}$.

2. X's consumption: $18	imes5	imes2.5=225$ and $20	imes3=60$. Total $=225+60=285$.

3. Y's consumption: $24	imes7=168$ and $30	imes6	imes0.75=135$. Total $=168+135=303$.

4. Share for X: $\dfrac{285}{285+303}=\dfrac{285}{588}=\dfrac{95}{196}$.

FINAL_ANSWER: b

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