The average of sales of a furniture shop in the years 2015, 2016, 2017, 2018 is Rs 16300, and that for years 2016, 2017, 2018, 2019 is Rs 18450. If the sales in 2019 are Rs 9200, then what are the sales in 2015?

Options

A. Rs 768
B. Rs 560
C. Rs 600
D. Rs 865

Answer

To solve the problem step by step, we need to find the sales in 2015 based on the given averages and the sales figure for 2019.

### Step 1: Calculate the total sales for the years 2015, 2016, 2017, and 2018.
The average sales for these four years is given as Rs 16,300.

Using the formula for average:
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
We can rearrange this to find the sum of observations:
\[ \text{Sum of observations} = \text{Average} \times \text{Number of observations} \]
For the years 2015 to 2018:
\[ \text{Sum}_{2015-2018} = 16300 \times 4 = 65200 \]

### Step 2: Calculate the total sales for the years 2016, 2017, 2018, and 2019.
The average sales for these four years is given as Rs 18,450.

Using the same formula:
\[ \text{Sum}_{2016-2019} = 18450 \times 4 = 73800 \]

### Step 3: Use the sales figure for 2019 to find the total sales for 2016, 2017, and 2018.
We know the sales in 2019 is Rs 9,200. Therefore, we can find the total sales for the years 2016, 2017, and 2018:
\[ \text{Sum}_{2016-2018} = \text{Sum}_{2016-2019} - \text{Sales in 2019} \]
\[ \text{Sum}_{2016-2018} = 73800 - 9200 = 64600 \]

### Step 4: Find the sales in 2015.
Now, we can find the sales in 2015 by subtracting the total sales for the years 2016, 2017, and 2018 from the total sales for the years 2015, 2016, 2017, and 2018:
\[ \text{Sales in 2015} = \text{Sum}_{2015-2018} - \text{Sum}_{2016-2018} \]
\[ \text{Sales in 2015} = 65200 - 64600 = 600 \]

### Final Answer:
The sales in 2015 are Rs 600.

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