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

Accepted Answer

16. Total money $= 352n$. When two persons receive Rs. 506 each, the amount remaining is $352n - 2(506) = 352n - 1012$. This remaining amount is divided equally among $n - 2$ persons, and each receives $\le 330$: $$\frac{352n - 1012}{n - 2} \le 330$$ $$352n - 1012 \le 330n - 660$$ $$22n \le 352$$ $$n \le 16$$ Therefore, the maximum possible value of $n$ is $16$.

Maximum number of persons for division of money

Explanation

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