Question

Two individuals, A and B, rent a pasture together. A has 18 horses that they graze for 4 months. B grazes 24 cows for 6 months and 36 sheep for 4 months. The following relationships are given: - 3 horses are equivalent to 6 cows, - 4 cows are equivalent to 8 sheep. What amount of rent should A pay ?

• A. 2/5
• B. 3/5
• C. 4/5
• D. 1/5

Answer 1

Answer:

A. 2/5

Let's calculate each person's share based on the amount of grazing used.

Convert all animals to a common unit

Given:

• 3 horses = 6 cows ⇒ 1 horse = 2 cows

• 4 cows = 8 sheep ⇒ 1 cow = 2 sheep

Therefore:

$1 \text{ horse} = 2 \text{ cows} = 4 \text{ sheep}$

Let's use sheep-equivalents.

Step 2: Calculate grazing usage

A's usage

18 horses for 4 months:

$18 \times 4 \times 4 = 288$

sheep-month units.

B's usage

24 cows for 6 months:

$24 \times 2 \times 6 = 288$

36 sheep for 4 months:

$36 \times 4 = 144$

Total for B:

$288 + 144 = 432$

Step 3: Find the rent ratio

A:B = 288:432 = 2:3

So A should pay $(\frac{2}{2+3}=\frac{2}{5})$ of the total rent.

Answer

A should pay$(\boxed{\frac{2}{5}})$ of the total rent (40%).