What is the difference between the average incomes of Jai to the average income of Veer throughout five years?
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An alternative, faster method:
Find the difference between their total sums first:
\[ 285 - 280 = 5\text{ thousand} \]
Then, simply divide this difference of totals by the number of years (5):
\[ \frac{5000}{5} = 1000 \]
This saves you from performing two separate divisions.
Step 1: Understanding the Concept:
To find the difference between the average incomes of two groups over the same period, we calculate the average income for each individual over the 5-year span and find the absolute difference between these averages. Key Formula or Approach:
The formulas are:
\[ \text{Average Income} = \frac{\text{Sum of incomes over 5 years}}{5} \]
\[ \text{Difference} = |\text{Average}_{\text{Jai}} - \text{Average}_{\text{Veer}}| \] Step 2: Detailed Explanation:
Let us sum and average the incomes for both individuals over all 5 years:
1. Jai (Jay):
- Incomes = 40, 45, 60, 60, 80 (in thousands)
\[ \text{Sum of Jai's Incomes} = 40 + 45 + 60 + 60 + 80 = 285\text{ thousand} \]
\[ \text{Average of Jai's Income} = \frac{285}{5} = 57\text{ thousand} = \text{Rs. } 57000 \]
2. Veer:
- Incomes = 60, 50, 70, 40, 60 (in thousands)
\[ \text{Sum of Veer's Incomes} = 60 + 50 + 70 + 40 + 60 = 280\text{ thousand} \]
\[ \text{Average of Veer's Income} = \frac{280}{5} = 56\text{ thousand} = \text{Rs. } 56000 \]
3. Calculate the difference:
\[ \text{Difference} = 57000 - 56000 = \text{Rs. } 1000 \]
This matches Option C. Step 3: Final Answer:
The difference between their average incomes is Rs. 1000.
