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 \(1^{st}\) and will get BDT 80; Durjoy has come \(2^{nd}\), Chopol is \(3^{rd}\), Billal is \(4^{th}\) 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 Chopol can receive?
A. 55, 15
B. 78, 5
C. 31, 14
D. 54, 15
Explanation: Chopol is \(3^{rd}\). So, Durjoy has to get more money than Chopol. Giving Anabi 5 and Billal 6 , the remaining 109 BDT can be distributed between Durjoy and Chopol as 55 and 54 BDT, respectively. So, the most Chopol can get is 54 BDT. For the least amount Chopol can get, firstly, Durjoy can get at most 79 BDT. That leaves 41 BDT where Chopol has to get more than Anabi and Bilal. So, numbers close to an arithmetic series will give the least amount for Chopol. The series will close to \(41/3\approx14\). The required series that meets the conditions is \(15, 14, 12\). So, the least amount Chopol can get is 15 .
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