Question

A grocer has a sale of Rs.6435, Rs.6927, Rs.6855, Rs.7230 and Rs.6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs.6500?
(a) Rs.4991
(b) Rs.5991
(c) Rs.6001
(d) Rs.6991

Answer 1

Hint: Average of n numbers ${{a}_{1}},{{a}_{2}},.............{{a}_{n}}$ can be given by formula
Average $=\dfrac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+.......{{a}_{n}}}{n}$ . Suppose price of the sixth sale as a variable and find the average of prices of sales of six months and equate it to the given average. Now, find the variables.

Complete step-by-step answer:
We know the average of n numbers can be given by adding them and hence dividing the sum by total numbers present i.e. by n. hence, we can get average of ${{a}_{1}},{{a}_{2}},{{a}_{3}}.............{{a}_{n}}$ as
Average $=\dfrac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+.......{{a}_{n}}}{n}$………………… (i)
Now, it is given that grocer has a sale of 6435, 6927, 6855, 7230 and 6562. For 5 consecutive months; so, we need to determine sales for next month such that the average of sales of six months be 6500Rs. So, let the sale in the sixth month be Rs.x. Hence, average of sales for all six months can be given using equation (i) as
Average = $=\dfrac{6435+6927+6855+7230+6562+x}{6}$
Average $=\dfrac{34009+x}{6}$ ………………. (ii)
Now, we know that the average sales of the whole six months is Rs.6500. Hence, we can equate $\dfrac{34009+x}{6}$ to 6500 as both are representing average sales for 6 consecutive months. So, we get
$\dfrac{6500}{1}=\dfrac{34009+x}{6}$
Now, on cross-multiplying the above equation, we get
$\begin{align}
  & 6500\times 6=34009+x \\
 & 39000=34009+x \\
\end{align}$
 So, value of x can be calculated as
$\begin{align}
  & x=39000-34009 \\
 & x=499\text{1 Rs}\text{.} \\
\end{align}$
So, we get sale for sixth month would be Rs.4991

So, the correct answer is “Option (a)”.

Note: Don’t calculate the average of the first five sales and then use it to find the average of it and the price of the sixth sale by adding them and dividing by 2. It is the wrong approach for the given question. Average given is the average of all six months sales price. So, be careful with these kinds of questions.
Take care while adding the given numbers. One may make mistakes here as well. So, take care of it while adding the given numbers. And don’t miss any number while writing the given numbers while taking average. Always cross-check by counting the numbers. So, be careful with it as well.