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Question

# A treasure is split between 5 explorers equally. Each explorer further divides his share of the treasure into 4 equal parts and pays one of those parts as tax. What fraction of the treasure do the 5 explorers together pay as tax ?

A
15th of the treasure
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B
14th of the treasure
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C
120th of the treasure
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D
116th of the treasure
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Solution

## The correct option is B 14th of the treasureWe convert each sentence of the question into a mathematical statement: Sentence 1: A treasure is split between 5 explorers equally Number of treasures=1 Number of explorers=5 ⟹Fraction of the treasure that each explorer gets=1÷5=15 Sentence 2: Each explorer further divideshis share of the treasure into 4 equalparts and pays one of those parts as tax. Share of the treasure that each explorer gets=15 Dividing the share into 4 equal parts=15÷4 Calculating 15÷4, we get: ∴The share of the treasure that each explorer pays as tax is 120 Sentence 3: What fraction of the treasuredo the 5 explorers together pay as tax ? Each explorer pays 120th of the wholetreasure as tax. ⟹Fraction of the treasure paid as tax by the 5 explorers together=5×120 Calculating 5×120, we get: 5 times 120=5×120=520 Now, 520=5÷520÷5=14 ∴The 5 explorers together pay 14th of the treasure as tax.

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