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A boy is playing in a lawn. There is an odd number of balls placed in the lawn at intervals of 1 m in a straight line. The boy is assembling the balls around the middle ball, while carrying only one ball at a time. The boy carried out the job starting with the ball in the middle, carrying balls in succession, thereby covering a distance of 364 m. What must be the number of balls in the lawn?
  • a)
    27
  • b)
    28
  • c)
    29
  • d)
    30
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A boy is playing in a lawn. There is an odd number of balls placed in ...
Let the number of balls be ‘n’.
As the boy covers 364 m, he covers 364/2 = 182 m on the one side and 182 m on the other side.
First consider the distance covered on one side: As the balls are placed in the lawn at intervals of 1 m in a straight line, so the total distance covered by him = 2 + (2+2) + (2+2+2) + (2+2+2+2) + ………. = 2 + 4 + 6 + 8 + ………… = n/2*2×2 + (n – 1) 2] = n(n+1) *Sum of ‘n’ terms in A.P. (arithmetic progression), Sn = n/2[2a + (n – 1) d],
where, n = number of terms, a = first term and d = common difference].
Here n is the number of balls or number of terms in the A.P. 
So, n(n+1) = 182 = 13×14
∴ n = 13.
Hence, the total number of balls = 13 + 13 + 1 = 27.
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Most Upvoted Answer
A boy is playing in a lawn. There is an odd number of balls placed in ...


Understanding the problem:
- The boy is assembling the balls around the middle ball while covering a distance of 364m.
- He carries only one ball at a time and starts with the middle ball.

Solution:
- Let the number of balls on one side of the middle ball be x.
- The total number of balls will be 1 (middle ball) + 2x (balls on both sides) = 2x + 1.
- The total distance covered will be the sum of distances of each ball from the middle ball.
- This forms an arithmetic progression with the first term as 0 (distance of the middle ball from itself) and common difference as 1.
- The sum of an arithmetic progression can be calculated using the formula: S = n/2 * (2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
- Therefore, 364 = (2x + 1)/2 * (0 + (2x + 1 - 1) * 1).
- Solving this equation, we get x = 13.
- Hence, the total number of balls = 2x + 1 = 2*13 + 1 = 27.

Therefore, the number of balls in the lawn is 27, which corresponds to option (a).
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A boy is playing in a lawn. There is an odd number of balls placed in the lawn at intervals of 1 m in a straight line. The boy is assembling the balls around the middle ball, while carrying only one ball at a time. The boy carried out the job starting with the ball in the middle, carrying balls in succession, thereby covering a distance of 364 m. What must be the number of balls in the lawn?a)27b)28c)29d)30Correct answer is option 'A'. Can you explain this answer?
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