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) 4991
B) 5991
C) 6001
D) 6991

Answer 1

Hint: In order to find the sales of the sixth month such that the average of grocery sales is equal to Rs.6500, assume the sixth month sale to be Rs $ x $ . Now calculate the sum of sales for six months and put this sum into the average formula $ avg. = \dfrac{{Sum\,}}{n} $ to obtain an equation in $ x $ .Solve the obtained equation to obtain the required answer.

Complete step-by-step answer:
We are given the sales of 5 consecutive months for a grocery shop as Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562.
Now to find the sixth month sale to have an average sale of Rs.6500,
Let us assume the sale of sixth month be $ x $ ,
Total sum of sales for six months=
 $
  sum = 6435 + 6927 + 6855 + 7230 + 6562 + x \\
  sum = 34009 + x \;
  $
Formula to calculate the average is
 $ avg. = \dfrac{{Sum\,}}{n} $
where n is the number of data terms., here in our case we have $ n = 6 $
putting the average sale as 6500, we have average as
 $ 6500 = \dfrac{{34009 + x}}{6} $
Multiplying both sides of the equation by the number $ 6 $ , we get
 $
  6500 \times 6 = \dfrac{{34009 + x}}{6} \times 6 \\
  39000 = 34009 + x \;
  $
Solving the above equation for variable $ x $ ,
 $
  x = 39000 - 34009 \\
  x = 4991 \;
  $
Therefore, the sales of the sixth month is equal to Rs $ 4991.So Correct option is (A).
So, the correct answer is “Option A”.

Note: 1. Avoid calculation errors. To cross check your answer take the help of a calculator for calculation purposes.
2. Average is also known as the mean of the data items.