Question

A student erroneously multiplied a number by 2/5 instead of 5/2. What is the percentage error in the calculation? *

Answer 1

Answer:-

Your Answer Is 84%.

Explanation:-

Given:-

• A student multiplied a number by $\tt\dfrac{2}{5}$ instead of $\dfrac{5}{2}$.

ToFind:-

• The percentage error in calculation.

Formula Used:-

$\\ \red{ \longrightarrow\underline{ \underline{ \blue{{\textbf{\% \: error = relative \: error \times 100. }}}}}}$

Now,

• Let the number which should be multiplied by $\bf\dfrac{2}{5}$ be x.

• So the correct answer would be $\bf\dfrac{5x}{2}.$

• But the answer of student will be $\bf\dfrac{2x}{5}.$

So,

The Absolute Error will be:-

$\\ \tt\mapsto \frac{5x}{2} - \frac{2x}{5} .$

$\\ \tt= \frac{(5x \times 5) - (2x \times 2)}{2 \times 5} \\ \\ \rm(by \: \: taking \: \: lcm).$

$\\ \bf \large = \frac{21x}{10} .$

Therefore Relative Error,

$\\ \tt = \dfrac{absolute \: \: error}{correct \: \: answer} .$

$\\ \tt = \large\dfrac{ \frac{21x}{10} }{ \frac{5x}{2} }$

$\\ \tt = \frac{21 \: \cancel{x}}{ \cancel{10}} \times \frac{ \cancel2}{5 \: \cancel {x}}.$

$\\ \tt = \frac{25}{5 \times 5} .$

$\\ \bf \large= \frac{21}{25} .$

And Hence,

$\\ \bf\mapsto \% \: error = relative \: \: error \times 100.$

$\\ \tt\mapsto \% \: error = \frac{21}{ \cancel{25}} \times \cancel{100}.$

$\\ \tt\mapsto \% \: error =21 \times 4.$

$\\ \large\red{\mapsto \boxed{ \blue{ \bf \% \: error =84 \%}}}.$

$\bf\therefore$ The Percentage Error In The Calculation Is Of 84%.

Answer 2

Answer:

84%

Step-by-step explanation:

Let the number be 10a.

 When it is multiplied by 2/5, it becomes 10a*2/5 = 4a

But actually it was to be: 10a*5/2 = 25a

Hence,

 Error = 25a - 4a = 21a

Error % = error/original * 100%

            = 21a/25a *100%

            = 21/25  * 100%

            = 84%