Question

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

• A. 15
• B. 17
• C. 16
• D. None of Above

Answer 1

The Correct Option is C

The problem states that:

"If a certain amount of money is divided equally among \(n\) persons, each one receives Rs 352."

Thus, the total amount of money is:

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

Next, we are told that:

"If two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receives less than or equal to Rs 330."

From this, we can calculate the total amount of money in two parts:

• First, two persons receive Rs 506 each, so the total amount for these two persons is \( 506 \times 2 = 1012 \).
• The remaining amount is \( 352n - 1012 \), and this remaining amount is divided equally among the remaining \( n - 2 \) persons, each receiving Rs 330 or less. Therefore, the total amount for the remaining persons is:

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

The total amount of money can thus be written as:

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

Expanding this expression:

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

Now, the total money is also equal to \( 352n \), so we equate the two expressions:

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

Next, simplify the inequality:

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

Rearranging the inequality gives:

\(22n \leq 352\)

Now, solving for \( n \):

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

\(n \leq 16\)

Thus, the maximum value that \( n \) can take is 16.

The correct option is (C): 16.