Question

In which year the production of tractors of all types taken together was approximately equal to the average of the total production during the period?

• A. 2012
• B. 2014
• C. 2016
• D. 2017
• A. 2013
• B. 2014
• C. 2017
• D. None of these
• A. A
• B. B
• C. C
• D. D
• A. D
• B. C
• C. B
• D. A
• A. 15
• B. 25
• C. 20
• D. 30

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
From the given data table, total production across all six years is computed to find the overall arithmetic mean.

Step 2: Key Formula or Approach:
Annual total production figures from 2012 to 2017 are:
- 2012: 74
- 2013: 71
- 2014: 75
- 2015: 90
- 2016: 80
- 2017: 86
Grand Total $= 74 + 71 + 75 + 90 + 80 + 86 = 476$.
Average production per year:
\[\text{Average} = \frac{476}{6} = 79.33 \approx 80\]

Step 3: Detailed Explanation:
In the year 2016, total tractor production was exactly 80, which is closest/equal to the average 79.33.

Step 4: Final Answer:
Therefore, the year is 2016.

Answer 2

Step 1: Understanding the Concept:
Evaluating the sum $(A + B)$ versus $(C + D)$ for each year listed in the options.

Step 2: Key Formula or Approach:
Calculating $(A+B)$ and $(C+D)$ for the given years:
- In 2013: $A+B = 20 + 10 = 30$; $C+D = 17 + 6 = 23$ ($30 \neq 23$).
- In 2014: $A+B = 16 + 14 = 30$; $C+D = 16 + 10 = 26$ ($30 \neq 26$).
- In 2017: $A+B = 6 + 14 = 20$; $C+D = 8 + 31 = 39$ ($20 \neq 39$).
(Note: In 2016, $A+B = 21+12=33$ and $C+D = 13+20=33$, but 2016 is not listed in options 1, 2, or 3).

Step 3: Detailed Explanation:
Since none of the years listed in options 1, 2, or 3 satisfies the equality condition, the correct choice is 'None of these'.

Step 4: Final Answer:
Hence, the correct option is (D) None of these.

Answer 3

Step 1: Understanding the Concept:
A continuous increase requires the annual production values to be strictly monotonically increasing from 2012 through 2017.

Step 2: Detailed Explanation:
Examining production trends for each tractor type:
- Type A: $8, 20, 16, 17, 21, 6$ (Decreases in 2014 and 2017).
- Type B: $16, 10, 14, 12, 12, 14$ (Fluctuates).
- Type C: $21, 17, 16, 15, 13, 8$ (Continuously decreases).
- Type D: $4 \to 6 \to 10 \to 16 \to 20 \to 31$ (Strictly increases every successive year).

Step 3: Final Answer:
Therefore, tractor type D exhibited a continuous increase in production.

Answer 4

Step 1: Understanding the Concept:
Calculating $25\%$ of total production in 2016 and comparing against individual tractor type outputs.

Step 2: Key Formula or Approach:
Total production of all types of tractors in 2016 was 80 units.
Calculating $25\%$ of 80:
\[25\% \text{ of } 80 = \frac{25}{100} \times 80 = 20\,\text{units}\]

Step 3: Detailed Explanation:
Checking production of each type in 2016:
- Type A: 21
- Type B: 12
- Type C: 13
- Type D: 20
Type D produced exactly 20 units.

Step 4: Final Answer:
Hence, type D tractors constituted 25% of total production in 2016.

Answer 5

Step 1: Understanding the Concept:
Percentage increase is calculated as the ratio of absolute increase to the base year value multiplied by 100.

Step 2: Key Formula or Approach:
From the table:
- Total production in 2014 (Base Year) $= 75\,\text{units}$.
- Total production in 2015 $= 90\,\text{units}$.
Absolute increase:
\[\Delta = 90 - 75 = 15\,\text{units}\]

Step 3: Detailed Explanation:
Percentage increase calculation:
\[\text{Percentage Increase} = \frac{15}{75} \times 100 = \frac{1}{5} \times 100 = 20\%\]

Step 4: Final Answer:
Therefore, the percentage increase was 20%.