Question : A boy found the answer to the question "subtract the sum of $\frac{1}{4}$ and $\frac{1}{5}$ from unity and express the answer in decimals" to be 0.45. The percentage of error in his answer was ________.
Option 1: $\frac{100}{11}$%
Option 2: $50$%
Option 3: $10$%
Option 4: $\frac{200}{11}$%
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Correct Answer: $\frac{200}{11}$%
Solution :
Given: A boy found the answer to the question "subtract the sum of $\frac{1}{4}$ and $\frac{1}{5}$ from unity and express the answer in decimals" to be 0.45.
If we subtract the sum of $\frac{1}{4}$ and $\frac{1}{5}$ from unity, we get,
$1 - (\frac{1}{4}+\frac{1}{5}) = 1-\frac{9}{20} = \frac{11}{20}= 0.55$
The boy's answer was 0.45.
So, the difference in answers (error) = (0.55 – 0.45) = 0.10
Therefore, the percentage of error $=(\frac{0.10}{0.55}) × 100 = \frac{10}{55} × 100 = \frac{200}{11}$%
Hence, the correct answer is $\frac{200}{11}$%.
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