My Olympiad problem solution 001

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aftab
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My Olympiad problem solution 001

Unread post by aftab » Tue Jan 03, 2012 9:25 pm

Three travelers came to a hotel and ordered for a pizza and fell asleep. The first traveler woke up and ate the 1/3 part of the pizza. The second traveler woke up and ate the1/3 part of the pizza. The third traveler woke up and did the same thing. In the morning they saw that the pizza remained on the table costs 8 taka. How much everyone will pay?

Ans. The first one cut the pizza into 3 pieces and ate 1 piece that means he ate 1/3 of the pizza. So that 2/3 of the pizza remained. The second person ate 1/3 of the 2/3 of the pizza that means 2/9 of the pizza. The two persons ate 5/9 of the pizza. The 4/9 part of the pizza remained. The third person ate 1/3 of the 4/9 of the pizza that means 4/27 of the pizza. So by the smallest piece, the first one ate 9 pieces, the second one ate 6 pieces and the third one ate 4 pieces. They all ate 19 pieces and 8 pieces remained. The 8 pieces costs 8 taka. So 1 piece costs 1 taka. So 27 pieces costs 27 taka that means the whole pizza costs 27 taka. The first one will pay 9 taka, the second one will pay 6 taka and the third one will pay 4 taka.

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