Question

How many years the production of castor is higher than the 90 percent of average production of cotton?

• A. 4
• B. 5
• C. 6
• D. 3

Hint:

Keep your intermediate numbers precise to avoid rounding errors when comparing values that are close to the threshold (such as 220 in 2014 vs the threshold of 223.71).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires us to calculate a threshold value based on the average cotton production and then count the number of years in which the castor production exceeds this threshold.
Key Formula or Approach:
1. Find the average production of cotton over all 7 years.
2. Calculate the threshold value (90% of the average cotton production).
3. Compare the castor production of each year against this threshold.

Step 2: Detailed Explanation:
Let us perform the calculations:
- Total cotton production over 7 years = 1740 Kgs.
- Average cotton production:
\[ \text{Average Cotton} = \frac{1740}{7} \approx 248.57\text{ Kgs} \]
- Threshold value (90% of average cotton):
\[ \text{Threshold} = 0.90 \times 248.57 \approx 223.71\text{ Kgs} \]
- Now, let us compare the castor production of each year against the threshold of 223.71 Kgs:
- 2011: 290 Kgs (\(> 223.71\)) \(\rightarrow\) Yes
- 2012: 230 Kgs (\(> 223.71\)) \(\rightarrow\) Yes
- 2013: 340 Kgs (\(> 223.71\)) \(\rightarrow\) Yes
- 2014: 220 Kgs (\(< 223.71\)) \(\rightarrow\) No
- 2015: 190 Kgs (\(< 223.71\)) \(\rightarrow\) No
- 2016: 180 Kgs (\(< 223.71\)) \(\rightarrow\) No
- 2017: 320 Kgs (\(> 223.71\)) \(\rightarrow\) Yes
- Counting the matching years, we get 4 years (2011, 2012, 2013, and 2017).

Step 3: Final Answer:
The production of castor is higher in 4 years (Option A).