Question

During which year the largest percentage of articles were defective out of the articles manufactured by unit III?

• A. 2014
• B. 2016
• C. 2018
• D. 2013
• A. \(16 \frac{9}{19}%\)
• B. \(16 \frac{11}{19}%\)
• C. \(15 \frac{11}{17}%\)
• D. \(12 \frac{9}{17}%\)
• A. 2013
• B. 2014
• C. 2015
• D. 2016

Answer 1

The Correct Option is C

Using the formula: \[ \text{Defective Percentage} = \left( \frac{D}{M} \right) \times 100 \] For each year: \[ \text{2013} = \left( \frac{28}{86} \right) \times 100 = 32.56% \] \[ \text{2014} = \left( \frac{14}{55} \right) \times 100 = 25.45% \] \[ \text{2015} = \left( \frac{6}{65} \right) \times 100 = 9.23% \] \[ \text{2016} = \left( \frac{10}{67} \right) \times 100 = 14.93% \] \[ \text{2017} = \left( \frac{12}{92} \right) \times 100 = 13.04% \] \[ \text{2018} = \left( \frac{22}{48} \right) \times 100 = 45.83% \] Since the highest defective percentage is 45.83% in 2018, the correct answer is 2018.

Answer 2

From the given data, the total number of manufactured and defective articles in 2017 are: \[ \text{Total Manufactured} = 80 + 82 + 92 + 58 + 68 = 380 \] \[ \text{Total Defective} = 21 + 3 + 12 + 17 + 10 = 63 \] Now, calculating the percentage: \[ \left( \frac{63}{380} \right) \times 100 = 16.58% \] Approximating to the nearest given option: \[ 16 \frac{9}{19}% \]
Thus, the correct answer is \(16 \frac{9}{19}%\).

Answer 3

We calculate the percentage increase or decrease using: \[ \text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \] For each year: - 2014: \[ \left( \frac{42 - 55}{55} \right) \times 100 = -23.64% \] % Option (Decrease) - 2015: \[ \left( \frac{58 - 42}{42} \right) \times 100 = 38.10% \] % Option (Increase) - 2016: \[ \left( \frac{78 - 58}{58} \right) \times 100 = 34.48% \] % Option (Increase) - 2017: \[ \left( \frac{82 - 78}{78} \right) \times 100 = 5.13% \] % Option (Increase) - 2018: \[ \left( \frac{66 - 82}{82} \right) \times 100 = -19.51% \] % Option (Decrease) The highest percentage change was in 2015 (38.10% increase).
Thus, the correct answer is 2015.