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A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?
Answer & Solution
Correct Answer:
Option
A
Actual result = 10x
By mistake it has been divided by 10 = $$\frac{x}{{10}}$$
%Change = $$ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} $$ × 100 = 99 = -99%
Since, actual value is greater than the wrong value.
Alternatively,
Let, x = 10
Actual result = 10 × 10 = 100
Wrong result = $$\frac{{10}}{{10}}$$ = 1
Change = (1 - 100) = -99
% Change = - 99%
By mistake it has been divided by 10 = $$\frac{x}{{10}}$$
%Change = $$ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} $$ × 100 = 99 = -99%
Since, actual value is greater than the wrong value.
Alternatively,
Let, x = 10
Actual result = 10 × 10 = 100
Wrong result = $$\frac{{10}}{{10}}$$ = 1
Change = (1 - 100) = -99
% Change = - 99%
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