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12 horses and 18 cows eat the grass of 6 acres in a certain time. How many acres will feed 18 horses and 12 cows for the same time, supposing a horse eats as much as 3 cows?
- a)22/3 acres
- b)39/8 acres
- c)40/11 acres
- d)25/9 acres
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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12 horses and 18 cows eat the grass of 6 acres in a certain time. How ...
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Given Information:
- 12 horses and 18 cows eat the grass of 6 acres in a certain time.
- A horse eats as much as 3 cows.
To Find:
- How many acres will feed 18 horses and 12 cows for the same time.
Solution:
Step 1: Calculate the total consumption of grass in acres for 12 horses and 18 cows
- Let the amount of grass consumed by one cow in a certain time be x acres.
- Then, the amount of grass consumed by one horse in the same time = 3x acres.
- Total grass consumed by 18 cows = 18x acres.
- Total grass consumed by 12 horses = 12 * 3x = 36x acres.
- Total grass consumed by 12 horses and 18 cows = 18x + 36x = 54x acres.
Step 2: Finding the amount of grass consumed by 1 horse and 1 cow
- Total grass consumed by 12 horses and 18 cows = 54x acres.
- This is consumed from 6 acres of grass.
- So, 54x = 6
- x = 6/54 = 1/9 acres
Step 3: Calculate the total consumption of grass in acres for 18 horses and 12 cows
- Total grass consumed by 18 horses = 18 * 3 * (1/9) = 6 acres
- Total grass consumed by 12 cows = 12 * 1/9 = 4/3 acres
- Total grass consumed by 18 horses and 12 cows = 6 + 4/3 = 18/3 + 4/3 = 22/3 acres
Therefore, 18 horses and 12 cows will eat the grass of 22/3 acres in the same time. Hence, option A is the correct answer.
- 12 horses and 18 cows eat the grass of 6 acres in a certain time.
- A horse eats as much as 3 cows.
To Find:
- How many acres will feed 18 horses and 12 cows for the same time.
Solution:
Step 1: Calculate the total consumption of grass in acres for 12 horses and 18 cows
- Let the amount of grass consumed by one cow in a certain time be x acres.
- Then, the amount of grass consumed by one horse in the same time = 3x acres.
- Total grass consumed by 18 cows = 18x acres.
- Total grass consumed by 12 horses = 12 * 3x = 36x acres.
- Total grass consumed by 12 horses and 18 cows = 18x + 36x = 54x acres.
Step 2: Finding the amount of grass consumed by 1 horse and 1 cow
- Total grass consumed by 12 horses and 18 cows = 54x acres.
- This is consumed from 6 acres of grass.
- So, 54x = 6
- x = 6/54 = 1/9 acres
Step 3: Calculate the total consumption of grass in acres for 18 horses and 12 cows
- Total grass consumed by 18 horses = 18 * 3 * (1/9) = 6 acres
- Total grass consumed by 12 cows = 12 * 1/9 = 4/3 acres
- Total grass consumed by 18 horses and 12 cows = 6 + 4/3 = 18/3 + 4/3 = 22/3 acres
Therefore, 18 horses and 12 cows will eat the grass of 22/3 acres in the same time. Hence, option A is the correct answer.
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12 horses and 18 cows eat the grass of 6 acres in a certain time. How many acres will feed 18 horses and 12 cows for the same time, supposing a horse eats as much as 3 cows?a) 22/3 acresb) 39/8 acresc) 40/11 acresd) 25/9 acrese)None of theseCorrect answer is option 'A'. Can you explain this answer?
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