Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for…
2025
Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 48 days?
- A.
45
- B.
35
- C.
60
- D.
30
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Correct answer: B
Answer: 35
Let G be the initial quantity of grass, r the grass growth per day, and c the amount one cow eats per day.
From 40 cows taking 40 days: G + 40r = 40 × 40c = 1600c.
From 30 cows taking 60 days: G + 60r = 30 × 60c = 1800c.
Subtract the first equation from the second: (G + 60r) − (G + 40r) = 1800c − 1600c ⇒ 20r = 200c ⇒ r = 10c.
Substitute r = 10c into G + 40r = 1600c: G + 40·10c = 1600c ⇒ G + 400c = 1600c ⇒ G = 1200c.
Let n be the number of cows needed to finish the grass in 48 days. Then G + 48r = 48·n·c.
Substitute G = 1200c and r = 10c: 1200c + 48·10c = 48n c ⇒ 1200c + 480c = 48n c ⇒ 1680c = 48n c.
Divide by 48c: n = 1680 ÷ 48 = 35.
Therefore 35 cows are needed.