Question

A and B share a rented field. A utilizes 20 horses for 5 months, while B uses 30 cows for 4 months and 45 sheep for 5 months. If 2 horses are equivalent to 5 cows, and 3 cows are equal to 9 sheep. What portion of the rent is A pay ?

• A. 20/89
• B. 30/89
• C. 40/89
• D. 50/89

Answer 1

Answer:

D. 50/89

The rent should be divided according to the equivalent animal-months used.

Step 1: Convert all animals to a common unit

Given:

• 2 horses = 5 cows ⇒ 1 horse = ( \frac{5}{2} ) cows

• 3 cows = 9 sheep ⇒ 1 cow = 3 sheep

Using cows as the common unit:

A's usage

20 horses for 5 months

$20 \times \frac{5}{2} = 50 \text{ cows}$

Cow-months:

$50 \times 5 = 250$
B's usage

30 cows for 4 months:

$30 \times 4 = 120$

45 sheep for 5 months:

$45 \text{ sheep} = \frac{45}{3} = 15 \text{ cows}$
$15 \times 5 = 75$

Total for B:

120 + 75 = 195

Step 2: Find the ratio of rent

A : B = 250 : 195 = 50 : 39
Total parts:

50 + 39 = 89
Therefore, A's share of the rent is

$\boxed{\frac{50}{89}}$

of the total rent.