Two individuals, P and Q, have rented a field. P keeps 18 horses in the field for 5 months and 12 cows for 3 months. Q adds 10 cows for 6 months and 36 sheep for 8 months. If 4 horses consume the same amount of food as 6 cows, and 8 cows eat as much as 12 sheep, what portion of the rent should P pay?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. .
Given, 4 horses = 6 cows
⇒ 1 horse = 6/4 = 1.5 cow-units.
8 cows = 12 sheep
⇒ 1 sheep = 8/12 = 2/3 cow-unit
For P: Horses: 18 horses for 5 months
⇒18 × 5 × 1.5 = 90 × 1.5 = 135 cow-month units.
Cows: 12 cows for 3 months
⇒ 12 × 3 × 1 = 361 cow-month units.
P total = 135 + 36 = 171 cow-month units
For Q: Cows: 10 cows for 6 months
⇒ 10 × 6 × 1 = 60 cow-month units.
Sheep: 36 sheep for 8 months
⇒ 36 × 8 × 2/3 = 288 × 2/3 = 192 cow-month units.
Q total = 60 +192 = 252 cow-month units.
Combined total = 171 + 252 = 423
P's share = 171/423 = 19/47