Question:medium

If a certain amount of money is divided equally among n persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of n is

Updated On: Jan 13, 2026
  • 15
  • 17
  • 16
  • None of Above
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The Correct Option is C

Solution and Explanation

The problem states that if a sum of money is distributed equally among \(n\) individuals, each person receives Rs 352. Consequently, the total sum of money is calculated as:

\(\text{Total amount} = 352 \times n = 352n\)

It is further stated that if two individuals each receive Rs 506, and the remaining sum is divided equally among the rest, each of these remaining individuals receives Rs 330 or less. This leads to the following calculations:

  • The total amount allocated to the first two individuals is \( 506 \times 2 = 1012 \).
  • The remaining sum is \( 352n - 1012 \). This sum is divided among the remaining \( n - 2 \) individuals, with each receiving no more than Rs 330. Therefore, the total amount for these remaining individuals is:

\(\text{Remaining amount} = (n - 2) \times 330\)

The total sum of money can also be expressed as:

\(\text{Total money} = 1012 + (n - 2) \times 330\)

Expanding this expression yields:

\(1012 + 330n - 660 = 352 + 330n\)

Equating this with the initial expression for total money (\( 352n \)):

\(352 + 330n \geq 352n\)

Simplifying the inequality:

\(330n \geq 352n - 352\)

Rearranging the terms gives:

\(22n \leq 352\)

Solving for \( n \):

\(n \leq \frac{352}{22}\)

\(n \leq 16\)

The maximum possible value for \( n \) is 16.

The correct option is (C): 16.

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