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

Given:

$4 \text{ cows} = 8 \text{ sheep}$

So,

$1 \text{ cow} = 2 \text{ sheep}$

Convert everything into sheep-units.

A's usage:

16 cows for 3 months

$16 \times 2 = 32 \text{ sheep-units}$

For 3 months:

$32 \times 3 = 96$

20 sheep for 4 months

$20 \times 4 = 80$

Total for A:

$96 + 80 = 176$

B's usage

30 sheep for 6 months

$30 \times 6 = 180$

Ratio of rent:

$A:B = 176:180 = 44:45$

Total parts:

$44+45=89$
Therefore, A’s share of the rent is:

$\boxed{\frac{44}{89}}$