Question

Two individuals, A and B, have rented a field. A places 21 horses in the field for 6 months and 15 cows for 2 months. B adds 15 cows for 6 months and 40 sheep for 7.5 months. If 3 horses consume the same amount of food as 5 cows, and 6 cows eat as much as 10 sheep, what portion of the rent should A cover?

• A. 8/17
• B. 19/17
• C. 16/17
• D. 20/17

Answer 1

Answer:

A. 8/17

Convert all animals into a common unit.

Given:

• $(3) horses (= 5) cows$
  
  $1 \text{ horse} = \frac{5}{3} \text{ cows}$
  

• $(6) cows (= 10) sheep$
  

  $1 \text{ sheep} = \frac{6}{10}=\frac{3}{5} \text{ cows}$
  

Now calculate consumption in cow-units × months.

A's usage

21 horses for 6 months

$21 \times \frac{5}{3}=35 \text{ cow-units}$

For 6 months:

$35 \times 6 = 210$

15 cows for 2 months

$15 \times 2 = 30$

Total for A:

$210+30=240$

B's usage

15 cows for 6 months

$15 \times 6 = 90$

40 sheep for 7.5 months

Each sheep (=\frac35) cow.

$40 \times \frac35 = 24 \text{ cow-units}$

For (7.5) months:

$24 \times 7.5 = 180$

Total for B:

90+180=270

Ratio of rent:

A:B = 240:270 = 8:9

Total parts:

8+9=17

Therefore, A should pay:

$\boxed{\frac{8}{17}}$

of the total rent.