A sum of BDT 200 will be divided among 5 swimmers, named Emran, Durjoy, Chopol, Billal and Anabi, who have just finished a swimming competition. Everyone will receive at least BDT 5 and no two swimmers will receive the same amount of money. Emran has come $1^{ ext {st }}$ and will get BDT 80; Durjoy has come $2^{ ext {nd }}$ , Chopol is $3^{ ext {rd }}$ , Billal is $4^{ ext {th }}$ and Anabi is last. Moreover, the distribution of money is subject to the following conditions:• No one will get any fractional amount of money.• The swimmer who finishes earlier must receive more money than the swimmer(s) he defeats.What are the greatest and least amount of money, consecutively, that Durjoy can receive?

Question

A sum of BDT 200 will be divided among 5 swimmers, named Emran, Durjoy, Chopol, Billal and Anabi, who have just finished a swimming competition. Everyone will receive at least BDT 5 and no two swimmers will receive the same amount of money. Emran has come $1^{	ext {st }}$ and will get BDT 80; Durjoy has come $2^{	ext {nd }}$ , Chopol is $3^{	ext {rd }}$ , Billal is $4^{	ext {th }}$ and Anabi is last. Moreover, the distribution of money is subject to the following conditions:• No one will get any fractional amount of money.• The swimmer who finishes earlier must receive more money than the swimmer(s) he defeats.What are the greatest and least amount of money, consecutively, that Durjoy can receive?

Accepted Answer

খ. 79. 32

ব্যাখ্যা: বাকি চারজনের মোট $120$। **দূর্জয় সর্বোচ্চ:** সে এমরানের (৮০) কম, তাই সর্বোচ্চ $79$; বাকি তিনজনের $41$ ভাগ হতে পারে (যেমন ২০, ১৫, ৬)। **সর্বনিম্ন:** বাকি তিনজনকে যতটা সম্ভব বড় করতে হবে: $D, D-1, D-2, D-3$; $4D-6 \le 120$ থেকে $D \ge 31.5$, তাই $D=32$ এবং ৩২, ৩১, ৩০, ২৭ (যোগফল ১২০) সম্ভব। অতএব (৭৯, ৩২)।

**শর্টকাট:** সর্বনিম্ন অংশের জন্য বাকিদের সমান-সমান (ক্রমিক) বড় ধরো।

**একই ধরনের প্রশ্ন:**
১. ১২০ টাকা ৩ জনের মধ্যে ভিন্ন পূর্ণসংখ্যায় ভাগ হলে সর্বোচ্চজনের ন্যূনতম অংশ কত?
*উত্তর:* ৪১ (৪১ + ৪০ + ৩৯ = ১২০)

প্রশ্ন ও সমাধান

সম্পর্কিত প্রশ্ন