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Defence Exam  >  Defence Questions  >  6153 plants are to be planted in a rectangula... Start Learning for Free
6153 plants are to be planted in a rectangular garden in such a manner that if number of plants in each row is 7 more than the number of plants in each column, still 3 plants remain to be planted. Find the number of columns in the garden.
  • a)
    75
  • b)
    82
  • c)
    123
  • d)
    150
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
6153 plants are to be planted in a rectangular garden in such a manner...
Since 3 plants are remaining, hence total plants that are arranged = 6153 - 3 = 6150
Since number of plants in each row is 7 more than the number of plants in each column;
Suppose ‘r’ and ‘c’ are the number of plants in each row and in each column respectively;
∴ r = c + 7
∴ c × (c + 7) = 6150
⇒ c2 + 7c - 6150 = 0
⇒ c2 + 82c - 75c - 6150 = 0
⇒ c(c + 82) - 75(c + 82) = 0
⇒ (c - 75)(c + 82) = 0
⇒ c = 75, -82
∴ Number of plants in each column = 75
Number of plants in each row = 75 + 7 = 82
∴ Number of columns in the garden = Number of plants in each row = 82
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Most Upvoted Answer
6153 plants are to be planted in a rectangular garden in such a manner...
To solve this problem, we can set up a system of equations based on the given information. Let's assume that the number of columns in the garden is C and the number of rows is R.

1. Set up the equations based on the given information:
- The total number of plants is 6153, so we have the equation: C * R = 6153.
- The number of plants in each row is 7 more than the number of plants in each column, so we have the equation: R = C + 7.

2. Substitute the second equation into the first equation:
- C * (C + 7) = 6153.
- Simplify the equation: C^2 + 7C - 6153 = 0.

3. Solve the quadratic equation:
- We can either factorize the equation or use the quadratic formula. Since factoring may not be easy in this case, let's use the quadratic formula.
- The quadratic formula is given by: C = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 7, and c = -6153.
- Plugging in the values, we get: C = (-7 ± √(7^2 - 4*1*(-6153))) / (2*1).
- Simplifying further, we have: C = (-7 ± √(49 + 24612)) / 2.
- C = (-7 ± √24661) / 2.
- C ≈ (-7 ± 157.01) / 2.

4. Find the possible values of C:
- We have two possible values for C: C ≈ (-7 + 157.01) / 2 ≈ 75 and C ≈ (-7 - 157.01) / 2 ≈ -82.
- Since the number of columns cannot be negative in this context, we discard the negative value.
- Therefore, the number of columns in the garden is approximately 75.

5. Choose the correct answer:
- The correct option is b) 82, which is the closest value to 75.

Therefore, the number of columns in the garden is 82.
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6153 plants are to be planted in a rectangular garden in such a manner that if number of plants in each row is 7 more than the number of plants in each column, still 3 plants remain to be planted. Find the number of columns in the garden.a)75b)82c)123d)150Correct answer is option 'B'. Can you explain this answer?
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