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Question : 17 of 39

Marks: +1, -0

A student on being asked to multiply

\frac{16}{17}

of a certain fraction made the mistake of dividing the fraction by

\frac{16}{17}

and so got an answer which exceeded the correct answer by

\frac{33}{340}

Find the correct answer.

$\frac{64}{85}$
$\frac{46}{58}$
$\frac{64}{58}$
None

Solution:

Concept:

Interpret the problem as finding the intended product of a fraction with

\frac{16}{17}

using the given error condition.

Explanation:

Let the certain fraction be

x

.

Correct answer:

\frac{16}{17} \times x

.

Mistaken answer:

x \div \frac{16}{17} = \frac{17}{16}x

.

Difference:

\frac{17}{16}x - \frac{16}{17}x = \frac{33}{340}

.

Compute left:

\left(\frac{17}{16} - \frac{16}{17}\right)x = \frac{289-256}{272}x = \frac{33}{272}x

.

So

\frac{33}{272}x = \frac{33}{340}

. Cancel

33

:

\frac{x}{272} = \frac{1}{340}

thus

x = \frac{272}{340} = \frac{68}{85}

.

Correct answer:

\frac{16}{17} \times \frac{68}{85} = \frac{16 \times 68}{17 \times 85} = \frac{16 \times 4}{85} = \frac{64}{85}

.

Answer:

\frac{64}{85}

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