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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 treasure
We 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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