A student multiplying a number by \frac{3}{5} instead of\frac{5}{3}, what is percentage error in 5 3the calculation?

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RRB GG Exam (Bhopal) 2009 click here to view all questions

A student multiplying a number by $\frac{3}{5}$ instead of $\frac{5}{3}$, what is percentage error in the calculation?

A0.44

B0.34

C0.54

D0.64

suraj ? Dec 17 '2019 at 21:37

Correct answer is: 0.64

Explanation:

Let the number be x.

Then, ideally he should have multiplied by  x by \(\frac{5}{3}\). Hence Correct result was \(x \times \frac{5}{3}= \frac{5x}{3}\). 

By mistake he multiplied x by \(\frac{3}{5}\) . Hence the result with error  = \(\frac{3x}{5} \)

Then, error = \(\big(\frac{5x}{3} - \frac{3x}{5}\big) = \frac{16x}{15} \)

\(\text{Error}   = \big(\frac{\text{error}}{\text{True vaue}}\big) \)

= \(\frac{\frac{16}{15} \times x}{ \frac{5}{3} \times x} \)

= 0.64

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Correct answer is: 0.64 Explanation: Let the number be x. Then, ideally he should have multiplied by  x by \(\frac{5}{3}\). Hence Correct result was \(x \times \frac{5}{3}= \frac{5x}{3}\).  By mistake he multiplied x by \(\frac{3}{5}\) . Hence the result with error  = \(\frac{3x}{5} \) Then, error = \(\big(\frac{5x}{3} - \frac{3x}{5}\big) = \frac{16x}{15} \) \(\text{Error}   = \big(\frac{\text{error}}{\text{True vaue}}\big) \) = \(\frac{\frac{16}{15} \times x}{ \frac{5}{3} \times x} \) = 0.64 suraj ? answered Dec 17 '2019 at 21:37 All Comments

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