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BECE Mathematics 2013 Paper

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Question : 30

Total: 40

If

15\%

of the length of a rope is 75 cm , find half of the length of the rope.

$500$ cm
$250$ cm
$\;\; 150 \; \mathrm{cm}$
$\;\; 100 \; \mathrm{cm}$

Solution:

Concept:

Half of the rope means

50\%

of its total length.

Explanation:

Given that

15\%

of the rope is

75\ \mathrm{cm}

.

Let the total length of the rope be

L

.

So,

15\% \text{ of } L = 75\ \mathrm{cm}

.

This means

\frac{15}{100}L = 75\ \mathrm{cm}

.

Therefore,

L = 75 \times \frac{100}{15} = 500\ \mathrm{cm}

.

Half of the rope is

\frac{1}{2} \times 500 = 250\ \mathrm{cm}

.

Alternatively, since

50\%

is required,

\frac{75 \times 50}{15} = 250\ \mathrm{cm}

.

Answer:

250\ \mathrm{cm}

, which is option B.

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