Question

Two individuals, A and B rent a pasture. A uses 16 cows for a duration of 3 months and 20 sheep for 4 months and B uses 30 sheep for 6 months. If 4 cows are equivalent to 8 sheep, determine A's portion of the rent.

• A. 44/89
• B. 54/89
• C. 64/89
• D. 74/89

Answer 1

Answer:

A. 44/89

Convert cows to sheep units: The problem states that 4 cows = 8 sheep. Therefore, 1 cow = 2 sheep.

• Calculate A's total usage in sheep units:

  • 16 cows for 3 months = $16 \times 2 \times 3 = 96$ sheep-months

  • 20 sheep for 4 months = $20 \times 4 = 80$ sheep-months

  • A's total consumption = $96 + 80 = \mathbf{176}$ sheep-months

• Calculate B's total usage: 30 sheep for 6 months = $30 \times 6 = \mathbf{180}$ sheep-months

• Find the rent sharing ratio (A : B): $176 : 180 = \mathbf{44 : 45}$

• Determine A's fractional share: A's share = $\frac{44}{44 + 45} = \mathbf{\frac{44}{89}}$ of the total rent.