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There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2 area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2 area of grass was grown, on which of the following days the lawn will be 100% green again?
- a)2nd day
- b)3rd day
- c)4th day
- d)5th day
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There is a 100% green lawn whose decrease in green area is directly pr...
►Let D be decrease in green area
►N1 be number of cows, G be growth in area and K1, K2 be constants.
►Also N2 be number of days
∴ D = K1N12 and G = K2N23
∴ When D = 8, N1 = 2
∴ K1 = 2
∴ D2 = 2(4)2 = 32
∴ K1 = 2
∴ D2 = 2(4)2 = 32
D3 = 2(6)2 = 72
D4 = 2(8)2 = 128
►Also, when G = 4, N2 = 1
∴ K2 = 4
∴ G2 = 4(2)3 = 32
∴ G2 = 4(2)3 = 32
G3 = 4(3)3 = 108
G4 = 4(4)3 = 256
►Hence, on third day, total lawn growth = 108 + 32 + 4 = 144 m2
►The total lawn decrease till the third day = 8 + 32 + 72 = 112 m2
►The total lawn growth is more than the lawn decreased until that day.
►Also, the growth rate of lawn is more than the decreasing of lawn from third day onwards.
►Hence, from 3rd day onwards lawn will be 100% green.
Hence, [2]
Hence, [2]
Most Upvoted Answer
There is a 100% green lawn whose decrease in green area is directly pr...
Understanding the problem:
- There is a 100% green lawn, and its decrease in green area is directly proportional to the square of the number of cows in the lawn.
- Two cows together ate 8m^2 of the lawn on the first day.
- Every day, two new cows join the existing cows.
- The growth of grass on the lawn is directly proportional to the cube of the number of days.
- At the end of the first day, 4m^2 area of grass was grown.
Calculating the rate of decrease in green area:
Let's assume the initial green area of the lawn is G0 and the number of cows on the first day is C0.
- The decrease in green area is directly proportional to the square of the number of cows. So, we can write it as:
Rate of decrease in green area = k1 * C^2
where k1 is the constant of proportionality.
- On the first day, two cows together ate 8m^2 area of the lawn. So, we can write it as:
k1 * C0^2 = 8
Calculating the rate of grass growth:
- The growth of grass on the lawn is directly proportional to the cube of the number of days. So, we can write it as:
Rate of grass growth = k2 * D^3
where k2 is the constant of proportionality and D is the number of days.
- At the end of the first day, 4m^2 area of grass was grown. So, we can write it as:
k2 * 1^3 = 4
Calculating the number of cows on a particular day:
Let's assume the number of cows on a particular day is C.
- On the first day, two cows together ate 8m^2 area of the lawn. So, we can write it as:
k1 * C0^2 = 8
- On the second day, two new cows join the existing cows. So, the total number of cows becomes C + 2. The decrease in green area is directly proportional to the square of the number of cows. So, we can write it as:
k1 * (C + 2)^2 = k1 * C^2 - 8
Calculating the number of days to make the lawn 100% green again:
- We need to find the number of days on which the lawn will be 100% green again, which means the green area will be equal to the initial green area (G0).
- Let's consider the second day, on which two new cows join the existing cows. The number of cows on the second day is C + 2.
- On the first day, the decrease in green area is k1 * C0^2.
- On the second day, the decrease in green area is k1 * (C + 2)^2 = k1 * C^2 - 8.
- The growth of grass on the second day is k2 * 2^3 = 8k2.
- To make the lawn 100% green again, the decrease in green area should be equal to the growth of grass. So, we can write it as:
k1
- There is a 100% green lawn, and its decrease in green area is directly proportional to the square of the number of cows in the lawn.
- Two cows together ate 8m^2 of the lawn on the first day.
- Every day, two new cows join the existing cows.
- The growth of grass on the lawn is directly proportional to the cube of the number of days.
- At the end of the first day, 4m^2 area of grass was grown.
Calculating the rate of decrease in green area:
Let's assume the initial green area of the lawn is G0 and the number of cows on the first day is C0.
- The decrease in green area is directly proportional to the square of the number of cows. So, we can write it as:
Rate of decrease in green area = k1 * C^2
where k1 is the constant of proportionality.
- On the first day, two cows together ate 8m^2 area of the lawn. So, we can write it as:
k1 * C0^2 = 8
Calculating the rate of grass growth:
- The growth of grass on the lawn is directly proportional to the cube of the number of days. So, we can write it as:
Rate of grass growth = k2 * D^3
where k2 is the constant of proportionality and D is the number of days.
- At the end of the first day, 4m^2 area of grass was grown. So, we can write it as:
k2 * 1^3 = 4
Calculating the number of cows on a particular day:
Let's assume the number of cows on a particular day is C.
- On the first day, two cows together ate 8m^2 area of the lawn. So, we can write it as:
k1 * C0^2 = 8
- On the second day, two new cows join the existing cows. So, the total number of cows becomes C + 2. The decrease in green area is directly proportional to the square of the number of cows. So, we can write it as:
k1 * (C + 2)^2 = k1 * C^2 - 8
Calculating the number of days to make the lawn 100% green again:
- We need to find the number of days on which the lawn will be 100% green again, which means the green area will be equal to the initial green area (G0).
- Let's consider the second day, on which two new cows join the existing cows. The number of cows on the second day is C + 2.
- On the first day, the decrease in green area is k1 * C0^2.
- On the second day, the decrease in green area is k1 * (C + 2)^2 = k1 * C^2 - 8.
- The growth of grass on the second day is k2 * 2^3 = 8k2.
- To make the lawn 100% green again, the decrease in green area should be equal to the growth of grass. So, we can write it as:
k1
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There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer?
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There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer?.
There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a 100% green lawn whose decrease in green area is directly proportional to the square of number of cows in the lawn. Two cows together ate 8m2area of lawn on the first day and everyday two new cows join them. The growth of grass on the lawn on a particular day is directly proportional to the cube of the number of days. If at the end of the first day, 4m2area of grass was grown, on which of the following days the lawn will be 100% green again?a)2nd day b)3rd day c)4th day d)5th dayCorrect answer is option 'B'. Can you explain this answer?.
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