If certain amount of money is divided equally among n person, 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 received less than or equal to Rs $330$ . Then, the maximum possible value of $n$ is

✅ Correct Option: 2

We have two different ways to distribute the same total amount of money:

Scenario 1: All n people get equal shares of Rs 352 each

Scenario 2: 2 people get Rs 506 each, and the remaining (n-2) people share the rest equally, getting ≤ Rs 330 each

Total amount of money = 352n (from Scenario 1)

In Scenario 2, this same amount is distributed as:

2 people get Rs 506 each = 2 × 506 = Rs 1012

Remaining (n-2) people get Rs y each = (n-2) × y

So: Total amount = 1012 + (n-2)y

Since both expressions equal the total amount:

352n = 1012 + (n-2)y

We solve for y (the amount each of the remaining people gets):

352n = 1012 + (n-2)y

352n - 1012 = (n-2)y

$y = \dfrac{352n - 1012}{n-2}$

We know that in Scenario 2, each of the remaining people gets ≤ Rs 330.

So: $y \leq 330$

$\dfrac{352n - 1012}{n-2} \leq 330$

Since n must be positive and greater than 2 (we need at least 2 people to take Rs 506 each), (n-2) > 0:

352n - 1012 ≤ 330(n-2)

352n - 1012 ≤ 330n - 660

352n - 330n ≤ 1012 - 660

22n ≤ 352

n ≤ 16

We also need n > 2 (since 2 people are getting Rs 506 each, there must be others to share the remaining amount).

Therefore: 2 < n ≤ 16

Since n must be a whole number (number of people), the maximum possible value is n = 16.

Answer: 16

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