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A student multiplied a number by ³/₅ instead of ³/₅.
What is the percentage error in the calculation?

134%
244%
354%
464%

Answer:- 4

Explanation:-

Solution:

\begin{aligned} Let the number be x . \\ Then, error = \frac{5}{3} x - \frac{3}{5} x = \frac{16}{15} x . \\ Error % = (\frac{16 x}{15} \times \frac{3}{5 x} \times 100) % \\ = 64 % . \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,x. \cr & {\text{Then,}}\,{\text{error}} = \frac{5}{3}x - \frac{3}{5}x = \frac{{16}}{{15}}x. \cr & {\text{Error}}\% = \left( {\frac{{16x}}{{15}} \times \frac{3}{{5x}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 64\% . \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let the number be x . \\ Then, error = \frac{5}{3} x - \frac{3}{5} x = \frac{16}{15} x . \\ Error % = (\frac{16 x}{15} \times \frac{3}{5 x} \times 100) % \\ = 64 % . \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,x. \cr & {\text{Then,}}\,{\text{error}} = \frac{5}{3}x - \frac{3}{5}x = \frac{{16}}{{15}}x. \cr & {\text{Error}}\% = \left( {\frac{{16x}}{{15}} \times \frac{3}{{5x}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 64\% . \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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