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:
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:
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:
Options
Answer: 16
Explanation:
Step 1: Express total money Total money = M Number of persons = n If divided equally: each gets Rs 352 So, M = 352 × n Step 2: Express money in the second scenario Money given to 2 persons: 2 × 506 = 1012 Remaining money: M – 1012 Remaining persons: n – 2 Each remaining person gets ≤ 330 So: (M – 1012) / (n – 2) ≤ 330 Step 3: Substitute M = 352 × n (352 × n – 1012) / (n – 2) ≤ 330 Multiply both sides by (n – 2): 352 × n – 1012 ≤ 330 × (n – 2) 352n – 1012 ≤ 330n – 660 352n – 330n ≤ 1012 – 660 22n ≤ 352 n ≤ 352 / 22 n ≤ 16 Step 4: Conclusion Maximum possible value of n = 16 ✅ Answer: 16
Explanation:
Step 1: Express total money Total money = M Number of persons = n If divided equally: each gets Rs 352 So, M = 352 × n Step 2: Express money in the second scenario Money given to 2 persons: 2 × 506 = 1012 Remaining money: M – 1012 Remaining persons: n – 2 Each remaining person gets ≤ 330 So: (M – 1012) / (n – 2) ≤ 330 Step 3: Substitute M = 352 × n (352 × n – 1012) / (n – 2) ≤ 330 Multiply both sides by (n – 2): 352 × n – 1012 ≤ 330 × (n – 2) 352n – 1012 ≤ 330n – 660 352n – 330n ≤ 1012 – 660 22n ≤ 352 n ≤ 352 / 22 n ≤ 16 Step 4: Conclusion Maximum possible value of n = 16 ✅ Answer: 16
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