Question

The monthly sales for the first 11 month of the year of a certain salesman were Rs. 12000 but due to his illness during the last month, the average sale for the whole year came down to Rs. 11,375. Find the value of the sale during the last month.

Answer 1

Hint: Assume the sales for the last month of the year be Rs. x. The monthly sales for the first 11 months of the year is Rs. 12000. Now, calculate the total amount sales for the first 11 months. The total amount of sales for 12 months will be the total amount of sales for the first 11 months and the amount of sales for the last month of the year. So, the total amount of the sales for 12 months is Rs. (x+132000). The average sale for the whole year is Rs. 11,375. We know the formula for average of sales, \[\text{Average sales =}\dfrac{\text{Total}\,\text{amount}\,\text{of}\,\text{sales}}{\text{Total}\,\text{number}\,\text{of}\,\text{months}}\] . Now, use this formula and get the value of x.

Complete step by step solution:
According to the question, we have the monthly sales for the first 11 month of the year of a certain salesman were Rs. 12000 but due to his illness during the last month, the average sale for the whole year came down to Rs. 11,375.
First of all, let us assume that the sales of the salesman during the last month of the year is Rs. x.
The amount of sales for the last month = Rs. x ………………………..(1)
The average sales for the whole year = Rs. 11,375 ………………………(2)
We have the monthly sales of the salesman for the first 11 month is Rs. 12000.
The total amount of sales for the first 11 month = Rs. \[11\times 12000\] = Rs. 132000 …………….(3)
The total amount of sales for 12 months will be the total amount of sales for the first 11 months and the amount of sales for the last month of the year.
From equation (1) and (3), we have the total amount of sales for the first 11 months and the amount of sales for the last month of the year.
So, the total amount of sales for 12 months = Rs. (x+132000) ………………….(4)
We know the formula for average of sales, \[\text{Average sales =}\dfrac{\text{Total}\,\text{amount}\,\text{of}\,\text{sales}}{\text{Total}\,\text{number}\,\text{of}\,\text{months}}\] …………………………..(5)
Here, the total number of months is 12.
From equation (2), we have the average sales for the whole year.
Now, putting the value of average sales from equation (2), total amount of sales from equation (4) and total number of months in equation (5), we get
\[\begin{align}
  & \text{11375 =}\dfrac{x+132000}{12} \\
 & \Rightarrow \text{11375}\times 12=x+132000 \\
 & \Rightarrow 136500=x+132000 \\
 & \Rightarrow 136500-132000=x \\
 & \Rightarrow 4500=x \\
\end{align}\]
Hence, the sales of the salesman for the last month of the year is Rs. 4500.

Note: We can also solve this question directly by using a formula.
Let the sales for the last month of the year be Rs x.
The average sales for 12 months = Rs. 11375.
The monthly sales for 11 months = Rs. 12000.
\[\begin{align}
  & \text{Average sales for 12 months =}\dfrac{11\times \text{monthly sales+sales of the 12th month}}{12} \\
 & \Rightarrow 11375=\dfrac{11\times 12000+x}{12} \\
 & \Rightarrow 11375\times 12=11\times 12000+x \\
 & \Rightarrow 136500=132000+x \\
 & \Rightarrow 136500-132000=x \\
 & \Rightarrow 4500=x \\
\end{align}\]
Hence, the sales of the salesman for the last month of the year is Rs. 4500.